(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 8.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[    251545,       6432]
NotebookOptionsPosition[    241996,       6113]
NotebookOutlinePosition[    242351,       6129]
CellTagsIndexPosition[    242308,       6126]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"0.9703", "-", "0.2387", "-", 
   RowBox[{"0.0353", " ", "0.0146"}]}], "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.547831273694158*^9, 3.547831298746951*^9}}],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"0.9983", "-", "0.0428", "-", "0.0387"}]}]], "Input",
 CellChangeTimes->{{3.547831300896823*^9, 3.547831342457506*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"q0", "=", "0.9990"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q1", "=", 
   RowBox[{"-", "0.0445"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q2", "=", 
   RowBox[{"-", "0.0102"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q3", "=", "0.0016"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q0", "=", "0.9983"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q1", "=", 
   RowBox[{"-", "0.0428"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q2", "=", 
   RowBox[{"-", "0.0387"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q3", "=", "0.0016"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "0.076"}], ",", " ", "0.084", ",", " ", "0.980"}], "}"}]}], 
  ";"}]}], "Input",
 CellChangeTimes->{{3.547831521044688*^9, 3.547831535672578*^9}, {
  3.547831986571528*^9, 3.547832038147975*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"q", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"q0", ",", " ", "q1", ",", "q2", ",", "q3"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"qa", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"0", ",", 
     RowBox[{"a", "[", 
      RowBox[{"[", "1", "]"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"[", "2", "]"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"[", "3", "]"}], "]"}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.547831319362134*^9, 3.547831396971871*^9}, {
  3.547831963990775*^9, 3.547832000658895*^9}}],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.547831899366419*^9, 3.54783191344567*^9}, 
   3.547831984846505*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Conjugate", "[", "q", "]"}], "**", "qa", "**", "q"}]], "Input",
 CellChangeTimes->{{3.5478313983486023`*^9, 3.547831406732046*^9}, {
  3.5478314634608307`*^9, 3.54783148401129*^9}, {3.547849613681897*^9, 
  3.547849639936575*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{
   RowBox[{"-", "2.168404344971009`*^-19"}], ",", "0.0003684218399999939`", 
   ",", 
   RowBox[{"-", "0.00018937463999998668`"}], ",", "0.9864609842399998`"}], 
  "]"}]], "Output",
 CellChangeTimes->{{3.54783146687459*^9, 3.547831484863453*^9}, {
  3.547849603005878*^9, 3.547849640386106*^9}}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.5478315484646053`*^9, 3.547831654311884*^9}, {
   3.5478317328894*^9, 3.547831733416306*^9}, 3.547875259115295*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"a", ".", "rotmat"}]], "Input",
 CellChangeTimes->{{3.547831663133204*^9, 3.5478316766689663`*^9}, {
  3.547831751907433*^9, 3.547831755890746*^9}, {3.547831920030751*^9, 
  3.547831949197816*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.0003684218399999939`", ",", 
   RowBox[{"-", "0.00004681739999999601`"}], ",", "0.9864609842399998`"}], 
  "}"}]], "Output",
 CellChangeTimes->{
  3.547831677466514*^9, {3.547831737140133*^9, 3.54783175646159*^9}, {
   3.5478319208269863`*^9, 3.547831950565077*^9}, 3.547832047372409*^9, 
   3.547849597252592*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"rotmat", ".", 
  RowBox[{"Transpose", "[", "rotmat", "]"}]}]], "Input",
 CellChangeTimes->{{3.547832058381922*^9, 3.547832063082708*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
    "0.9998699642276003`", ",", "2.0053051759914842`*^-7", ",", "0.`"}], 
    "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"2.0053051759914842`*^-7", ",", "1.003254391003432`", ",", 
     RowBox[{"-", "0.0001452358226552014`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.`", ",", 
     RowBox[{"-", "0.0001452358226552014`"}], ",", "0.9998699642276001`"}], 
    "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.547832063467564*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"md", "=", 
     RowBox[{"Import", "[", 
      RowBox[{
      "\"\<~/quadrotor/fenino/log_mag_d.dat\>\"", ",", " ", "\"\<Table\>\""}],
       "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"mr", "=", 
     RowBox[{"Import", "[", 
      RowBox[{
      "\"\<~/quadrotor/fenino/log_mag_r.dat\>\"", ",", " ", "\"\<Table\>\""}],
       "]"}]}], ";"}]}]}]], "Input",
 CellChangeTimes->{{3.547849430553343*^9, 3.547849469831307*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"avg", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"For", "[", 
   RowBox[{
    RowBox[{"i", "=", "1"}], ",", " ", 
    RowBox[{"i", "\[LessEqual]", 
     RowBox[{"Length", "[", "md", "]"}]}], ",", 
    RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"q", "=", 
      RowBox[{"Quaternion", "[", 
       RowBox[{
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", " ", 
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "3"}], "]"}], "]"}], ",", " ", 
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "4"}], "]"}], "]"}], ",", 
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "5"}], "]"}], "]"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"q", "=", 
      RowBox[{"q", "/", 
       RowBox[{"Norm", "[", "q", "]"}]}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"avg", "+=", "q"}], ";"}]}], "\[IndentingNewLine]", "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avg", "/=", 
   RowBox[{"Length", "[", "md", "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.547850376861328*^9, 3.5478503978451633`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"field", "=", 
    RowBox[{"{", "}"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"For", "[", 
   RowBox[{
    RowBox[{"i", "=", "1"}], ",", " ", 
    RowBox[{"i", "\[LessEqual]", 
     RowBox[{"Length", "[", "md", "]"}]}], ",", 
    RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"a", "=", 
      RowBox[{"Quaternion", "[", 
       RowBox[{"0", ",", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "3"}], "]"}], "]"}], ",", " ", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "4"}], "]"}], "]"}], ",", " ", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "5"}], "]"}], "]"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", "\[IndentingNewLine]", 
     RowBox[{"m", "=", 
      RowBox[{"Quaternion", "[", 
       RowBox[{"0", ",", " ", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "6"}], "]"}], "]"}], ",", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "7"}], "]"}], "]"}], ",", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "8"}], "]"}], "]"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", 
     RowBox[{"ae", "=", 
      RowBox[{
       RowBox[{"Conjugate", "[", "avg", "]"}], "**", "m", "**", "avg"}]}], 
     ";", "\[IndentingNewLine]", 
     RowBox[{"AppendTo", "[", 
      RowBox[{"field", ",", " ", 
       RowBox[{"Norm", "[", "m", "]"}]}], "]"}], ";"}]}], 
   "\[IndentingNewLine]", "]"}], ";"}], "\[IndentingNewLine]", "av"}], "Input",\

 CellChangeTimes->{{3.5478494796175823`*^9, 3.547849587377473*^9}, {
  3.5478496463413486`*^9, 3.547849747004159*^9}, {3.5478502619494543`*^9, 
  3.54785026813983*^9}, {3.547850327718691*^9, 3.547850406136447*^9}, {
  3.54785090991551*^9, 3.547850931441834*^9}}],

Cell[BoxData["av"], "Output",
 CellChangeTimes->{
  3.547850408906289*^9, {3.5478509179073544`*^9, 3.54785093173405*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["field"], "Input",
 CellChangeTimes->{{3.5478509199346333`*^9, 3.547850920210096*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.9751209999999999`", ",", "0.973713`", ",", "0.982257`", ",", "0.983133`",
    ",", "0.986009`", ",", "0.988293`", ",", "0.9814489999999999`", ",", 
   "0.973061`", ",", "0.9869089999999999`", ",", "0.9828250000000001`", ",", 
   "0.9823409999999999`", ",", "0.987485`", ",", "0.9808969999999999`", ",", 
   "0.9763369999999999`", ",", "0.9851489999999999`", ",", "0.987125`", ",", 
   "0.9846010000000001`", ",", "0.9881329999999999`", ",", 
   "0.9963770000000001`", ",", "0.992069`", ",", "0.971937`", ",", 
   "0.987934`", ",", "0.9811329999999999`", ",", "0.979073`", ",", 
   "0.9955010000000001`", ",", "0.996677`", ",", "0.990378`", ",", 
   "0.992069`", ",", "0.985409`", ",", "0.9972610000000001`", ",", 
   "0.986293`", ",", "0.9894850000000001`", ",", "0.979949`", ",", 
   "0.9814489999999999`", ",", "0.997763`", ",", "0.9796889999999999`", ",", 
   "0.979149`", ",", "0.989501`", ",", "0.987485`", ",", 
   "0.9878099999999999`", ",", "0.982474`", ",", "0.983133`", ",", 
   "0.984374`", ",", "0.984341`", ",", "0.9973139999999999`", ",", 
   "0.9920819999999999`", ",", "0.979457`", ",", "0.988001`", ",", 
   "0.9850500000000001`", ",", "0.9951789999999999`", ",", 
   "0.9811329999999999`", ",", "0.99813`", ",", "0.985709`", ",", "0.983133`",
    ",", "0.994969`", ",", "0.9903770000000001`", ",", 
   "0.9886010000000001`"}], "}"}]], "Output",
 CellChangeTimes->{{3.547850920506555*^9, 3.547850934447852*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Mean", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.5478509365099382`*^9, 3.547850938451639*^9}}],

Cell[BoxData["0.9860120350877196`"], "Output",
 CellChangeTimes->{3.547850938834201*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"StandardDeviation", "[", "field", "]"}]], "Input",
 CellChangeTimes->{{3.547850940675866*^9, 3.547850948790393*^9}}],

Cell[BoxData["0.00649918241551778`"], "Output",
 CellChangeTimes->{{3.5478509451344013`*^9, 3.547850949008762*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Norm", "[", "q", "]"}]], "Input",
 CellChangeTimes->{{3.547849723262232*^9, 3.547849724125762*^9}}],

Cell[BoxData["0.99976815`"], "Output",
 CellChangeTimes->{3.547849724498948*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["ae"], "Input",
 CellChangeTimes->{{3.547850237775519*^9, 3.5478502378541737`*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{
   RowBox[{"-", "6.938893903907228`*^-18"}], ",", 
   RowBox[{"-", "0.0803702722349778`"}], ",", "0.41635070442094824`", ",", 
   RowBox[{"-", "0.8995845063289389`"}]}], "]"}]], "Output",
 CellChangeTimes->{3.547850238148518*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"FQ", "[", "qqq_", "]"}], "=", 
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"Im", "[", 
      RowBox[{"Hold", "[", 
       RowBox[{
        RowBox[{"FromQuaternion", "[", "qqq", "]"}], "/.", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"J", "\[Rule]", "0"}], ",", 
          RowBox[{"K", "\[Rule]", "0"}]}], "}"}]}], "]"}], "]"}], ",", 
     RowBox[{"Re", "[", 
      RowBox[{"Hold", "[", 
       RowBox[{
        RowBox[{"FromQuaternion", "[", "qqq", "]"}], "/.", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"J", "\[Rule]", "1"}], ",", 
          RowBox[{"K", "\[Rule]", "0"}]}], "}"}]}], "]"}], "]"}], ",", 
     RowBox[{"Re", "[", 
      RowBox[{"Hold", "[", 
       RowBox[{
        RowBox[{"FromQuaternion", "[", "qqq", "]"}], "/.", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"J", "\[Rule]", "0"}], ",", 
          RowBox[{"K", "\[Rule]", "1"}]}], "}"}]}], "]"}], "]"}]}], "}"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.547849946784409*^9, 3.547850154740266*^9}, {
  3.547850222773472*^9, 3.547850223939309*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ListPlot", "[", 
  RowBox[{"field", "[", 
   RowBox[{"[", 
    RowBox[{"All", ",", "2"}], "]"}], "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.547849694658763*^9, 3.547849694966714*^9}, {
  3.5478502476055193`*^9, 3.547850314925241*^9}, {3.547850419140792*^9, 
  3.547850422497693*^9}}],

Cell[BoxData[
 GraphicsBox[
  {Hue[0.67, 0.6, 0.6], PointBox[CompressedData["
1:eJxTTMoPSmViYGCwBGIQDQEf7Ce43bVKrt62HyrgsO+t+VmOmu1QPoeD1t/o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    "]]},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, Automatic},
  PlotRange->Automatic,
  PlotRangeClipping->True]], "Output",
 CellChangeTimes->{{3.547850273056566*^9, 3.547850316213665*^9}, {
  3.547850416135412*^9, 3.547850422816596*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Mean", "[", "field", "]"}]], "Input",
 CellChangeTimes->{{3.547850437123309*^9, 3.547850438784745*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0", ",", 
   RowBox[{"-", "0.08816847738835225`"}], ",", "0.4101876065033563`", ",", 
   RowBox[{"-", "0.9000740740698108`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.5478504391619053`*^9}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{"mxy", "=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"Mean", "[", "field", "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}], "^", "2"}], "+", 
     RowBox[{
      RowBox[{
       RowBox[{"Mean", "[", "field", "]"}], "[", 
       RowBox[{"[", "3", "]"}], "]"}], "^", "2"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mz", "=", 
   RowBox[{"Abs", "[", 
    RowBox[{
     RowBox[{"Mean", "[", "field", "]"}], "[", 
     RowBox[{"[", "4", "]"}], "]"}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.547850444967908*^9, 3.547850481385662*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"ArcTan", "[", 
    RowBox[{"48608.", "/", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"19321", "^", "2"}], "+", 
       RowBox[{"5170", "^", "2"}]}], "]"}]}], "]"}], "/", "Pi"}], "*", 
  "180"}]], "Input",
 CellChangeTimes->{{3.547850609333818*^9, 3.547850665587823*^9}}],

Cell[BoxData["67.63428909536627`"], "Output",
 CellChangeTimes->{{3.547850630495822*^9, 3.547850666144841*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"38", "/", "60."}]], "Input",
 CellChangeTimes->{{3.547850677970825*^9, 3.5478506795067263`*^9}}],

Cell[BoxData["0.6333333333333333`"], "Output",
 CellChangeTimes->{3.547850679892542*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"%", "//", "Degree"}]], "Input",
 CellChangeTimes->{{3.547850646650145*^9, 3.547850647819499*^9}}],

Cell[BoxData[
 RowBox[{"\[Degree]", "[", "1.1804410319598386`", "]"}]], "Output",
 CellChangeTimes->{3.547850648035613*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["Degree"], "Input",
 CellChangeTimes->{{3.5478506316042147`*^9, 3.547850636028187*^9}}],

Cell[BoxData["\[Degree]"], "Output",
 CellChangeTimes->{3.547850636940144*^9}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{"md", "=", 
   RowBox[{"Import", "[", 
    RowBox[{
    "\"\<~/quadrotor/fenino/log_m_4_d.dat\>\"", ",", " ", "\"\<Table\>\""}], 
    "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mr", "=", 
   RowBox[{"Import", "[", 
    RowBox[{
    "\"\<~/quadrotor/fenino/log_m_4_r.dat\>\"", ",", " ", "\"\<Table\>\""}], 
    "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avg", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avga", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avgm", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"For", "[", 
   RowBox[{
    RowBox[{"i", "=", "1"}], ",", " ", 
    RowBox[{"i", "\[LessEqual]", 
     RowBox[{"Length", "[", "md", "]"}]}], ",", 
    RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"q", "=", 
      RowBox[{"Quaternion", "[", 
       RowBox[{
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", " ", 
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "3"}], "]"}], "]"}], ",", " ", 
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "4"}], "]"}], "]"}], ",", 
        RowBox[{"mr", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "5"}], "]"}], "]"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"q", "=", 
      RowBox[{"q", "/", 
       RowBox[{"Norm", "[", "q", "]"}]}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"avg", "+=", "q"}], ";", "\[IndentingNewLine]", 
     "\[IndentingNewLine]", 
     RowBox[{"avga", "+=", 
      RowBox[{"Quaternion", "[", 
       RowBox[{"0", ",", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "3"}], "]"}], "]"}], ",", " ", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "4"}], "]"}], "]"}], ",", " ", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "5"}], "]"}], "]"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"avgm", "+=", 
      RowBox[{"Quaternion", "[", 
       RowBox[{"0", ",", " ", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "6"}], "]"}], "]"}], ",", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "7"}], "]"}], "]"}], ",", 
        RowBox[{"md", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "8"}], "]"}], "]"}]}], "]"}]}], ";"}]}], 
   "\[IndentingNewLine]", "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avg", "/=", 
   RowBox[{"Length", "[", "md", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avga", "/=", 
   RowBox[{"Length", "[", "md", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"avgm", "/=", 
    RowBox[{"Length", "[", "md", "]"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"avga", "=", 
    RowBox[{"Quaternion", "[", 
     RowBox[{"0", ",", "1", ",", "5", ",", "2"}], "]"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avg", "/=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"Norm", "[", "avg", "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avga", "/=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"Norm", "[", "avga", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avgm", "/=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"Norm", "[", "avgm", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"field", "=", 
    RowBox[{"{", "}"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"q0", "=."}], ";", 
  RowBox[{"q1", "=."}], ";", 
  RowBox[{"q2", "=."}], ";", 
  RowBox[{"q3", "=."}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"q", "=", 
    RowBox[{"Quaternion", "[", 
     RowBox[{"q0", ",", "q1", ",", "q2", ",", "q3"}], "]"}]}], ";"}], 
  "\[IndentingNewLine]", "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avga", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"0", ",", "a1", ",", "a2", ",", "a3"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"avgm", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"0", ",", "m1", ",", "m2", ",", "m3"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"refm", "=", 
    RowBox[{"Quaternion", "[", 
     RowBox[{"0", ",", "r1", ",", "r2", ",", "r3"}], "]"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"erra", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"erra0", ",", "erra1", ",", "erra2", ",", "erra3"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"errm", "=", 
   RowBox[{"Quaternion", "[", 
    RowBox[{"errm0", ",", "errm1", ",", "errm2", ",", "errm3"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"qerra", "=", 
   RowBox[{"Norm", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"Conjugate", "[", "q", "]"}], "**", "avga", "**", "q"}], "-", 
     RowBox[{"Quaternion", "[", 
      RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"qerrm", "=", 
   RowBox[{"Norm", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"Conjugate", "[", "q", "]"}], "**", "avgm", "**", "q"}], "-", 
     "refm"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"f", "=", 
   RowBox[{"qerra", "+", "qerrm"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"qerra", "=", 
   RowBox[{
    RowBox[{"q", "**", 
     RowBox[{"Quaternion", "[", 
      RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "]"}], "**", 
     RowBox[{"Conjugate", "[", "q", "]"}]}], "-", "avga"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"qerrm", "=", 
   RowBox[{
    RowBox[{"q", "**", "refm", "**", 
     RowBox[{"Conjugate", "[", "q", "]"}]}], "-", "avgm"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"chi2", "=", 
    RowBox[{"Sum", "[", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{"qerra", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "^", "2"}], "/", 
        RowBox[{
         RowBox[{"erra", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "^", "2"}]}], "+", 
       RowBox[{
        RowBox[{
         RowBox[{"qerrm", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "^", "2"}], "/", 
        RowBox[{
         RowBox[{"errm", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "^", "2"}]}]}], ",", 
      RowBox[{"{", 
       RowBox[{"i", ",", "1", ",", "4"}], "}"}]}], "]"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"(*", "\[IndentingNewLine]", 
   RowBox[{"parmin", "=", 
    RowBox[{"NMinimize", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"f", ",", 
        RowBox[{
         RowBox[{"-", "1"}], "\[LessEqual]", "q0", "\[LessEqual]", "1"}], ",", 
        RowBox[{
         RowBox[{"-", "1"}], "\[LessEqual]", "q1", "\[LessEqual]", "1"}], ",", 
        RowBox[{
         RowBox[{"-", "1"}], "\[LessEqual]", "q2", "\[LessEqual]", "1"}], ",", 
        RowBox[{
         RowBox[{"-", "1"}], "\[LessEqual]", "q3", "\[LessEqual]", "1"}]}], 
       "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"q0", ",", "q1", ",", "q2", ",", "q3"}], "}"}]}], "]"}]}], " ",
    "\[IndentingNewLine]", "*)"}]}]}], "Input",
 CellChangeTimes->CompressedData["
1:eJwdzV0og3EYBfAZ295Z+2j1qlksZalps5S4kDYX0kKRlhtLW5MiS02Z1rQb
aTXfsQuUwqR2YZPcMBPRasqWkmJJxJr5aEVZ4z3/i6dfp07nqTDbuqxsFotV
xhzUzavdHFtKn7ceTsFtvtMLlWH5MmzyS1egYayeuDrbvg5beKYTmPVm43B3
yJSA6c3XP3jpW+JwGafpRjEsjt0RVWt0KdQ8Dcph5UGdDWbeb+2QnqAEPPxz
GMUwHb13w43xPLFD5ZqCL73aGRgVzgWg0RIhmhY9QahgJ2KQSoWu4EVo/x52
+Ts+oehX+QUDdP4b2kdqf2CkIJwjOTlQSDFK1DQF1bwGIdxzhaVwR8iXQY2m
swoWnbqJHtG1Gh7NPtZQZPdGB6tLjvUwfjb6Brub2zLwI9n3UY7+c45oGJax
FIyCBwex1efjwoXtfj6c1BYaodMi64VbunMzlPQELfAf12PORA==
  "]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Conjugate", "[", "avg", "]"}], "**", "avga", "**", 
  "avg"}]], "Input",
 CellChangeTimes->{{3.5478751906275997`*^9, 3.547875220442441*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"1.3877787807814457`*^-17", ",", "0.000171409331732153`", ",", 
   RowBox[{"-", "0.0002974155019501105`"}], ",", "0.9999999410814281`"}], 
  "]"}]], "Output",
 CellChangeTimes->{{3.547875201317992*^9, 3.5478752114144497`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"avg", "**", "avga", "**", 
  RowBox[{"Conjugate", "[", "avg", "]"}]}]], "Input",
 CellChangeTimes->{{3.547875227004396*^9, 3.547875234138802*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"2.7755575615628914`*^-17", ",", 
   RowBox[{"-", "0.44908868991987455`"}], ",", 
   RowBox[{"-", "0.5745910534655105`"}], ",", 
   RowBox[{"-", "0.6842254525106801`"}]}], "]"}]], "Output",
 CellChangeTimes->{3.547875234520418*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", "avga"}]], "Input",
 CellChangeTimes->{{3.5478752652258463`*^9, 3.547875320235364*^9}, {
  3.54787566678684*^9, 3.547875667019087*^9}, {3.5478757420753107`*^9, 
  3.547875767036532*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Transpose", "[", "rotmat", "]"}], ".", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"avga", "[", 
     RowBox[{"[", "2", "]"}], "]"}], ",", 
    RowBox[{"avga", "[", 
     RowBox[{"[", "3", "]"}], "]"}], ",", 
    RowBox[{"avga", "[", 
     RowBox[{"[", "4", "]"}], "]"}]}], "}"}]}]], "Input",
 CellChangeTimes->{{3.5478753005560627`*^9, 3.5478753808256273`*^9}, {
  3.547875773190673*^9, 3.547875783189886*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.0001714093317320975`", ",", 
   RowBox[{"-", "0.0002974155019501712`"}], ",", "0.9999999410814281`"}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.547875308541102*^9, 3.547875381291112*^9}, 
   3.54787566886938*^9, {3.5478757713937883`*^9, 3.54787578352003*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["avg"], "Input",
 CellChangeTimes->{{3.547873553687723*^9, 3.547873560536042*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"0.8264620226513903`", ",", "0.536003124247001`", ",", 
   RowBox[{"-", "0.14450179959371384`"}], ",", 
   RowBox[{"-", "0.09370381970125118`"}]}], "]"}]], "Output",
 CellChangeTimes->{{3.547873554837694*^9, 3.5478735608887167`*^9}}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"chi2", ";"}]], "Input",
 CellChangeTimes->{{3.5478729662910748`*^9, 3.5478729665738277`*^9}, 
   3.5479204705101633`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"qerr", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"2", "/", 
      RowBox[{"D", "[", 
       RowBox[{"chi2", ",", 
        RowBox[{"{", 
         RowBox[{"q0", ",", "2"}], "}"}]}], "]"}]}], ",", 
     RowBox[{"2", "/", 
      RowBox[{"D", "[", 
       RowBox[{"chi2", ",", 
        RowBox[{"{", 
         RowBox[{"q1", ",", "2"}], "}"}]}], "]"}]}], ",", 
     RowBox[{"2", "/", 
      RowBox[{"D", "[", 
       RowBox[{"chi2", ",", 
        RowBox[{"{", 
         RowBox[{"q2", ",", "2"}], "}"}]}], "]"}]}], ",", 
     RowBox[{"2", "/", 
      RowBox[{"D", "[", 
       RowBox[{"chi2", ",", 
        RowBox[{"{", 
         RowBox[{"q3", ",", "2"}], "}"}]}], "]"}]}]}], "}"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.547873022064516*^9, 3.547873125074317*^9}, {
   3.547873604168193*^9, 3.5478736330421057`*^9}, 3.5478737104458313`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"qerr", "/.", 
   RowBox[{"parmin", "[", 
    RowBox[{"[", "2", "]"}], "]"}]}], "/.", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"erra1", "\[Rule]", "0.00751"}], ",", 
    RowBox[{"erra2", "\[Rule]", "0.00674"}], ",", 
    RowBox[{"erra3", "\[Rule]", "0.00907"}], ",", 
    RowBox[{"errm1", "\[Rule]", "0.007"}], ",", 
    RowBox[{"errm2", "\[Rule]", "0.007"}], ",", 
    RowBox[{"errm3", "\[Rule]", "0.007"}]}], "}"}]}]], "Input",
 CellChangeTimes->{{3.547873711401659*^9, 3.5478737629294653`*^9}, {
  3.5479202874303017`*^9, 3.547920315581718*^9}}],

Cell[CellGroupData[{

Cell[BoxData["qerr"], "Input",
 CellChangeTimes->{{3.547921190355443*^9, 3.547921190827745*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"2", "/", 
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q1", "2"]}], 
       SuperscriptBox["erra2", "2"]], "+", 
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q2", "2"]}], 
       SuperscriptBox["erra1", "2"]], "+", 
      FractionBox[
       RowBox[{
        RowBox[{"8", " ", 
         SuperscriptBox["q0", "2"]}], "+", 
        RowBox[{"4", " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "a3"}], "+", 
           SuperscriptBox["q0", "2"], "-", 
           SuperscriptBox["q1", "2"], "-", 
           SuperscriptBox["q2", "2"], "+", 
           SuperscriptBox["q3", "2"]}], ")"}]}]}], 
       SuperscriptBox["erra3", "2"]], "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm1", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q0", " ", "r1"}], "-", 
             RowBox[{"2", " ", "q3", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q2", " ", "r3"}]}], ")"}], "2"]}], "+", 
         RowBox[{"4", " ", "r1", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m1"}], "+", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm2", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q3", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q0", " ", "r2"}], "-", 
             RowBox[{"2", " ", "q1", " ", "r3"}]}], ")"}], "2"]}], "+", 
         RowBox[{"4", " ", "r2", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m2"}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm3", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "2"}], " ", "q2", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q1", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q0", " ", "r3"}]}], ")"}], "2"]}], "+", 
         RowBox[{"4", " ", "r3", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m3"}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], 
     ")"}]}], ",", 
   RowBox[{"2", "/", 
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q0", "2"]}], 
       SuperscriptBox["erra2", "2"]], "+", 
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q3", "2"]}], 
       SuperscriptBox["erra1", "2"]], "+", 
      FractionBox[
       RowBox[{
        RowBox[{"8", " ", 
         SuperscriptBox["q1", "2"]}], "-", 
        RowBox[{"4", " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "a3"}], "+", 
           SuperscriptBox["q0", "2"], "-", 
           SuperscriptBox["q1", "2"], "-", 
           SuperscriptBox["q2", "2"], "+", 
           SuperscriptBox["q3", "2"]}], ")"}]}]}], 
       SuperscriptBox["erra3", "2"]], "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm1", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q1", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q2", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q3", " ", "r3"}]}], ")"}], "2"]}], "+", 
         RowBox[{"4", " ", "r1", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m1"}], "+", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm2", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q2", " ", "r1"}], "-", 
             RowBox[{"2", " ", "q1", " ", "r2"}], "-", 
             RowBox[{"2", " ", "q0", " ", "r3"}]}], ")"}], "2"]}], "-", 
         RowBox[{"4", " ", "r2", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m2"}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm3", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q3", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q0", " ", "r2"}], "-", 
             RowBox[{"2", " ", "q1", " ", "r3"}]}], ")"}], "2"]}], "-", 
         RowBox[{"4", " ", "r3", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m3"}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], 
     ")"}]}], ",", 
   RowBox[{"2", "/", 
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q0", "2"]}], 
       SuperscriptBox["erra1", "2"]], "+", 
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q3", "2"]}], 
       SuperscriptBox["erra2", "2"]], "+", 
      FractionBox[
       RowBox[{
        RowBox[{"8", " ", 
         SuperscriptBox["q2", "2"]}], "-", 
        RowBox[{"4", " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "a3"}], "+", 
           SuperscriptBox["q0", "2"], "-", 
           SuperscriptBox["q1", "2"], "-", 
           SuperscriptBox["q2", "2"], "+", 
           SuperscriptBox["q3", "2"]}], ")"}]}]}], 
       SuperscriptBox["erra3", "2"]], "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm1", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "2"}], " ", "q2", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q1", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q0", " ", "r3"}]}], ")"}], "2"]}], "-", 
         RowBox[{"4", " ", "r1", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m1"}], "+", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm2", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q1", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q2", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q3", " ", "r3"}]}], ")"}], "2"]}], "+", 
         RowBox[{"4", " ", "r2", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m2"}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm3", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "2"}], " ", "q0", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q3", " ", "r2"}], "-", 
             RowBox[{"2", " ", "q2", " ", "r3"}]}], ")"}], "2"]}], "-", 
         RowBox[{"4", " ", "r3", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m3"}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], 
     ")"}]}], ",", 
   RowBox[{"2", "/", 
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q1", "2"]}], 
       SuperscriptBox["erra1", "2"]], "+", 
      FractionBox[
       RowBox[{"8", " ", 
        SuperscriptBox["q2", "2"]}], 
       SuperscriptBox["erra2", "2"]], "+", 
      FractionBox[
       RowBox[{
        RowBox[{"8", " ", 
         SuperscriptBox["q3", "2"]}], "+", 
        RowBox[{"4", " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "a3"}], "+", 
           SuperscriptBox["q0", "2"], "-", 
           SuperscriptBox["q1", "2"], "-", 
           SuperscriptBox["q2", "2"], "+", 
           SuperscriptBox["q3", "2"]}], ")"}]}]}], 
       SuperscriptBox["erra3", "2"]], "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm1", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "2"}], " ", "q3", " ", "r1"}], "-", 
             RowBox[{"2", " ", "q0", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q1", " ", "r3"}]}], ")"}], "2"]}], "-", 
         RowBox[{"4", " ", "r1", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m1"}], "+", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm2", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q0", " ", "r1"}], "-", 
             RowBox[{"2", " ", "q3", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q2", " ", "r3"}]}], ")"}], "2"]}], "-", 
         RowBox[{"4", " ", "r2", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m2"}], "-", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
      "+", 
      RowBox[{
       RowBox[{"1", "/", 
        SuperscriptBox["errm3", "2"]}], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", "q1", " ", "r1"}], "+", 
             RowBox[{"2", " ", "q2", " ", "r2"}], "+", 
             RowBox[{"2", " ", "q3", " ", "r3"}]}], ")"}], "2"]}], "+", 
         RowBox[{"4", " ", "r3", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "m3"}], "+", 
            RowBox[{"q0", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q2"}], " ", "r1"}], "+", 
               RowBox[{"q1", " ", "r2"}], "+", 
               RowBox[{"q0", " ", "r3"}]}], ")"}]}], "+", 
            RowBox[{"q1", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", " ", "r1"}], "+", 
               RowBox[{"q0", " ", "r2"}], "-", 
               RowBox[{"q1", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q2", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", " ", "r1"}], "-", 
               RowBox[{"q3", " ", "r2"}], "+", 
               RowBox[{"q2", " ", "r3"}]}], ")"}]}], "-", 
            RowBox[{"q3", " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "q1"}], " ", "r1"}], "-", 
               RowBox[{"q2", " ", "r2"}], "-", 
               RowBox[{"q3", " ", "r3"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], 
     ")"}]}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.547873721941371*^9, 3.547873763339872*^9, 3.547873844538336*^9, {
   3.547920316518792*^9, 3.547920397916325*^9}, 3.547920472684354*^9, {
   3.5479210996137657`*^9, 3.5479211399474983`*^9}, 3.5479211911182127`*^9, 
   3.547921292957759*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FullSimplify", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.547921204075054*^9, 3.547921255126863*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"2", "/", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"(", 
        RowBox[{"8", "*", 
         RowBox[{"q1", "^", "2"}]}], ")"}], "/", 
       RowBox[{"erra2", "^", "2"}]}], " ", "+", " ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"8", "*", 
         RowBox[{"q2", "^", "2"}]}], ")"}], "/", 
       RowBox[{"erra1", "^", "2"}]}], " ", "-", " ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"4", "*", 
         RowBox[{"(", 
          RowBox[{"a3", " ", "-", " ", 
           RowBox[{"3", "*", 
            RowBox[{"q0", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"q1", "^", "2"}], " ", "+", " ", 
           RowBox[{"q2", "^", "2"}], " ", "-", " ", 
           RowBox[{"q3", "^", "2"}]}], ")"}]}], ")"}], "/", 
       RowBox[{"erra3", "^", "2"}]}], " ", "+", " ", "\n", "    ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"1", "/", 
         RowBox[{"errm1", "^", "2"}]}], ")"}], "*", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "4"}], "*", "r1", "*", 
          RowBox[{"(", 
           RowBox[{"m1", " ", "+", " ", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"-", "3"}], "*", 
                RowBox[{"q0", "^", "2"}]}], " ", "-", " ", 
               RowBox[{"q1", "^", "2"}], " ", "+", " ", 
               RowBox[{"q2", "^", "2"}], " ", "+", " ", 
               RowBox[{"q3", "^", "2"}]}], ")"}], "*", "r1"}]}], ")"}]}], " ",
          "+", " ", 
         RowBox[{"8", "*", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"q1", "*", "q2"}], " ", "-", " ", 
            RowBox[{"3", "*", "q0", "*", "q3"}]}], ")"}], "*", "r1", "*", 
          "r2"}], " ", "+", " ", "\n", "      ", 
         RowBox[{"8", "*", 
          RowBox[{"q3", "^", "2"}], "*", 
          RowBox[{"r2", "^", "2"}]}], " ", "+", " ", 
         RowBox[{"8", "*", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"3", "*", "q0", "*", "q2", "*", "r1"}], " ", "+", " ", 
            RowBox[{"q1", "*", "q3", "*", "r1"}], " ", "-", " ", 
            RowBox[{"2", "*", "q2", "*", "q3", "*", "r2"}]}], ")"}], "*", 
          "r3"}], " ", "+", " ", 
         RowBox[{"8", "*", 
          RowBox[{"q2", "^", "2"}], "*", 
          RowBox[{"r3", "^", "2"}]}]}], ")"}]}], " ", "+", " ", "\n", "    ", 
      
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"8", "*", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{"q2", "*", "r1"}], " ", "-", " ", 
             RowBox[{"q1", "*", "r2"}]}], ")"}], "^", "2"}]}], " ", "-", " ", 
         
         RowBox[{"4", "*", "m3", "*", "r3"}], " ", "+", " ", 
         RowBox[{"8", "*", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{
             RowBox[{"-", "3"}], "*", "q0", "*", "q2", "*", "r1"}], " ", "+", 
            " ", 
            RowBox[{"q1", "*", "q3", "*", "r1"}], " ", "+", " ", 
            RowBox[{"3", "*", "q0", "*", "q1", "*", "r2"}], " ", "+", " ", 
            RowBox[{"q2", "*", "q3", "*", "r2"}]}], ")"}], "*", "r3"}], " ", 
         "-", " ", "\n", "      ", 
         RowBox[{"4", "*", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{
             RowBox[{"-", "3"}], "*", 
             RowBox[{"q0", "^", "2"}]}], " ", "+", " ", 
            RowBox[{"q1", "^", "2"}], " ", "+", " ", 
            RowBox[{"q2", "^", "2"}], " ", "-", " ", 
            RowBox[{"q3", "^", "2"}]}], ")"}], "*", 
          RowBox[{"r3", "^", "2"}]}]}], ")"}], "/", 
       RowBox[{"errm3", "^", "2"}]}], " ", "+", " ", "\n", "    ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"1", "/", 
         RowBox[{"errm2", "^", "2"}]}], ")"}], "*", 
       RowBox[{"(", 
        RowBox[{"4", "*", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"r2", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", "m2"}], " ", "+", " ", 
              RowBox[{"2", "*", "q1", "*", "q2", "*", "r1"}], " ", "+", " ", 
              RowBox[{"3", "*", 
               RowBox[{"q0", "^", "2"}], "*", "r2"}], " ", "-", " ", 
              RowBox[{
               RowBox[{"q1", "^", "2"}], "*", "r2"}], " ", "+", " ", 
              RowBox[{
               RowBox[{"q2", "^", "2"}], "*", "r2"}]}], ")"}]}], " ", "+", 
           " ", "\n", "       ", 
           RowBox[{
            RowBox[{"q3", "^", "2"}], "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", "*", 
               RowBox[{"r1", "^", "2"}]}], " ", "-", " ", 
              RowBox[{"r2", "^", "2"}]}], ")"}]}], " ", "-", " ", 
           RowBox[{"6", "*", "q0", "*", "q1", "*", "r2", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", 
            RowBox[{"q1", "^", "2"}], "*", 
            RowBox[{"r3", "^", "2"}]}], " ", "+", " ", "\n", "       ", 
           RowBox[{"2", "*", "q3", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"3", "*", "q0", "*", "r1", "*", "r2"}], " ", "-", " ", 
              RowBox[{"2", "*", "q1", "*", "r1", "*", "r3"}], " ", "+", " ", 
              RowBox[{"q2", "*", "r2", "*", "r3"}]}], ")"}]}]}], ")"}]}], 
        ")"}]}]}], ")"}]}], ",", " ", "\n", "  ", 
   RowBox[{"1", "/", 
    RowBox[{"(", 
     RowBox[{"2", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{"2", "*", 
           RowBox[{"q0", "^", "2"}]}], ")"}], "/", 
         RowBox[{"erra2", "^", "2"}]}], " ", "+", " ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"2", "*", 
           RowBox[{"q3", "^", "2"}]}], ")"}], "/", 
         RowBox[{"erra1", "^", "2"}]}], " ", "+", " ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"a3", " ", "-", " ", 
           RowBox[{"q0", "^", "2"}], " ", "+", " ", 
           RowBox[{"3", "*", 
            RowBox[{"q1", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"q2", "^", "2"}], " ", "-", " ", 
           RowBox[{"q3", "^", "2"}]}], ")"}], "/", 
         RowBox[{"erra3", "^", "2"}]}], " ", "+", " ", "\n", "     ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"2", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q3", "*", "r1"}], " ", "+", " ", 
               RowBox[{"q0", "*", "r2"}]}], ")"}], "^", "2"}]}], " ", "+", 
           " ", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{"m3", " ", "+", " ", 
              RowBox[{"2", "*", "q0", "*", "q2", "*", "r1"}], " ", "-", " ", 
              RowBox[{"6", "*", "q1", "*", "q3", "*", "r1"}], " ", "-", " ", 
              RowBox[{"6", "*", "q0", "*", "q1", "*", "r2"}], " ", "-", " ", 
              RowBox[{"2", "*", "q2", "*", "q3", "*", "r2"}]}], ")"}], "*", 
            "r3"}], " ", "-", " ", "\n", "       ", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{
              RowBox[{"q0", "^", "2"}], " ", "-", " ", 
              RowBox[{"3", "*", 
               RowBox[{"q1", "^", "2"}]}], " ", "-", " ", 
              RowBox[{"q2", "^", "2"}], " ", "+", " ", 
              RowBox[{"q3", "^", "2"}]}], ")"}], "*", 
            RowBox[{"r3", "^", "2"}]}]}], ")"}], "/", 
         RowBox[{"errm3", "^", "2"}]}], " ", "+", " ", "\n", "     ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"1", "/", 
           RowBox[{"errm1", "^", "2"}]}], ")"}], "*", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            RowBox[{"(", 
             RowBox[{"-", "m1"}], ")"}], "*", "r1"}], " ", "+", " ", 
           RowBox[{
            RowBox[{"q0", "^", "2"}], "*", 
            RowBox[{"r1", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"3", "*", 
            RowBox[{"q1", "^", "2"}], "*", 
            RowBox[{"r1", "^", "2"}]}], " ", "-", " ", 
           RowBox[{
            RowBox[{"q2", "^", "2"}], "*", 
            RowBox[{"r1", "^", "2"}]}], " ", "-", " ", 
           RowBox[{
            RowBox[{"q3", "^", "2"}], "*", 
            RowBox[{"r1", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"6", "*", "q1", "*", "q2", "*", "r1", "*", "r2"}], " ", 
           "+", " ", "\n", "       ", 
           RowBox[{"2", "*", 
            RowBox[{"q2", "^", "2"}], "*", 
            RowBox[{"r2", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"6", "*", "q1", "*", "q3", "*", "r1", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"4", "*", "q2", "*", "q3", "*", "r2", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", 
            RowBox[{"q3", "^", "2"}], "*", 
            RowBox[{"r3", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"2", "*", "q0", "*", "r1", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{"(", 
                RowBox[{"-", "q3"}], ")"}], "*", "r2"}], " ", "+", " ", 
              RowBox[{"q2", "*", "r3"}]}], ")"}]}]}], ")"}]}], " ", "+", " ", 
        "\n", "     ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"1", "/", 
           RowBox[{"errm2", "^", "2"}]}], ")"}], "*", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"r2", "*", 
            RowBox[{"(", 
             RowBox[{"m2", " ", "-", " ", 
              RowBox[{"2", "*", "q0", "*", "q3", "*", "r1"}], " ", "-", " ", 
              RowBox[{
               RowBox[{"q0", "^", "2"}], "*", "r2"}], " ", "+", " ", 
              RowBox[{"3", "*", 
               RowBox[{"q1", "^", "2"}], "*", "r2"}], " ", "+", " ", 
              RowBox[{
               RowBox[{"q3", "^", "2"}], "*", "r2"}]}], ")"}]}], " ", "+", 
           " ", 
           RowBox[{
            RowBox[{"q2", "^", "2"}], "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", "*", 
               RowBox[{"r1", "^", "2"}]}], " ", "-", " ", 
              RowBox[{"r2", "^", "2"}]}], ")"}]}], " ", "+", " ", "\n", 
           "       ", 
           RowBox[{"6", "*", "q0", "*", "q1", "*", "r2", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", 
            RowBox[{"q0", "^", "2"}], "*", 
            RowBox[{"r3", "^", "2"}]}], " ", "-", " ", 
           RowBox[{"2", "*", "q2", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"3", "*", "q1", "*", "r1", "*", "r2"}], " ", "+", " ", 
              RowBox[{"2", "*", "q0", "*", "r1", "*", "r3"}], " ", "+", " ", 
              RowBox[{"q3", "*", "r2", "*", "r3"}]}], ")"}]}]}], ")"}]}]}], 
       ")"}]}], ")"}]}], ",", " ", "\n", "  ", 
   RowBox[{"1", "/", 
    RowBox[{"(", 
     RowBox[{"2", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{"2", "*", 
           RowBox[{"q0", "^", "2"}]}], ")"}], "/", 
         RowBox[{"erra1", "^", "2"}]}], " ", "+", " ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"2", "*", 
           RowBox[{"q3", "^", "2"}]}], ")"}], "/", 
         RowBox[{"erra2", "^", "2"}]}], " ", "+", " ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"a3", " ", "-", " ", 
           RowBox[{"q0", "^", "2"}], " ", "+", " ", 
           RowBox[{"q1", "^", "2"}], " ", "+", " ", 
           RowBox[{"3", "*", 
            RowBox[{"q2", "^", "2"}]}], " ", "-", " ", 
           RowBox[{"q3", "^", "2"}]}], ")"}], "/", 
         RowBox[{"erra3", "^", "2"}]}], " ", "+", " ", "\n", "     ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"2", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{
               RowBox[{"q0", "*", "r1"}], " ", "-", " ", 
               RowBox[{"q3", "*", "r2"}]}], ")"}], "^", "2"}]}], " ", "+", 
           " ", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{"m3", " ", "-", " ", 
              RowBox[{"2", "*", 
               RowBox[{"(", 
                RowBox[{
                 RowBox[{
                  RowBox[{"-", "3"}], "*", "q0", "*", "q2", "*", "r1"}], " ", 
                 "+", " ", 
                 RowBox[{"q1", "*", "q3", "*", "r1"}], " ", "+", " ", 
                 RowBox[{"q0", "*", "q1", "*", "r2"}], " ", "+", " ", 
                 RowBox[{"3", "*", "q2", "*", "q3", "*", "r2"}]}], ")"}]}]}], 
             ")"}], "*", "r3"}], " ", "-", " ", "\n", "       ", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{
              RowBox[{"q0", "^", "2"}], " ", "-", " ", 
              RowBox[{"q1", "^", "2"}], " ", "-", " ", 
              RowBox[{"3", "*", 
               RowBox[{"q2", "^", "2"}]}], " ", "+", " ", 
              RowBox[{"q3", "^", "2"}]}], ")"}], "*", 
            RowBox[{"r3", "^", "2"}]}]}], ")"}], "/", 
         RowBox[{"errm3", "^", "2"}]}], " ", "+", " ", "\n", "     ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"1", "/", 
           RowBox[{"errm2", "^", "2"}]}], ")"}], "*", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"r2", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", "m2"}], " ", "+", " ", 
              RowBox[{"2", "*", "q0", "*", "q3", "*", "r1"}], " ", "+", " ", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"q0", "^", "2"}], " ", "+", " ", 
                 RowBox[{"3", "*", 
                  RowBox[{"q2", "^", "2"}]}], " ", "-", " ", 
                 RowBox[{"q3", "^", "2"}]}], ")"}], "*", "r2"}]}], ")"}]}], 
           " ", "+", " ", 
           RowBox[{
            RowBox[{"q1", "^", "2"}], "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", "*", 
               RowBox[{"r1", "^", "2"}]}], " ", "-", " ", 
              RowBox[{"r2", "^", "2"}]}], ")"}]}], " ", "+", " ", "\n", 
           "       ", 
           RowBox[{"6", "*", "q2", "*", "q3", "*", "r2", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", 
            RowBox[{"q3", "^", "2"}], "*", 
            RowBox[{"r3", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"q1", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"6", "*", "q2", "*", "r1", "*", "r2"}], " ", "+", " ", 
              RowBox[{"4", "*", "q3", "*", "r1", "*", "r3"}], " ", "-", " ", 
              RowBox[{"2", "*", "q0", "*", "r2", "*", "r3"}]}], ")"}]}]}], 
          ")"}]}], " ", "+", " ", "\n", "     ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"1", "/", 
           RowBox[{"errm1", "^", "2"}]}], ")"}], "*", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"m1", "*", "r1"}], " ", "-", " ", 
           RowBox[{
            RowBox[{"q1", "^", "2"}], "*", 
            RowBox[{"r1", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"3", "*", 
            RowBox[{"q2", "^", "2"}], "*", 
            RowBox[{"r1", "^", "2"}]}], " ", "+", " ", 
           RowBox[{
            RowBox[{"q3", "^", "2"}], "*", 
            RowBox[{"r1", "^", "2"}]}], " ", "-", " ", 
           RowBox[{"6", "*", "q1", "*", "q2", "*", "r1", "*", "r2"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", 
            RowBox[{"q1", "^", "2"}], "*", 
            RowBox[{"r2", "^", "2"}]}], " ", "-", " ", "\n", "       ", 
           RowBox[{"2", "*", "q1", "*", "q3", "*", "r1", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", "q0", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"q3", "*", "r1", "*", "r2"}], " ", "-", " ", 
              RowBox[{"3", "*", "q2", "*", "r1", "*", "r3"}], " ", "+", " ", 
              RowBox[{"2", "*", "q1", "*", "r2", "*", "r3"}]}], ")"}]}], " ", 
           "-", " ", 
           RowBox[{
            RowBox[{"q0", "^", "2"}], "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"r1", "^", "2"}], " ", "-", " ", 
              RowBox[{"2", "*", 
               RowBox[{"r3", "^", "2"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], 
     ")"}]}], ",", " ", "\n", "  ", 
   RowBox[{"2", "/", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"(", 
        RowBox[{"8", "*", 
         RowBox[{"q1", "^", "2"}]}], ")"}], "/", 
       RowBox[{"erra1", "^", "2"}]}], " ", "+", " ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"8", "*", 
         RowBox[{"q2", "^", "2"}]}], ")"}], "/", 
       RowBox[{"erra2", "^", "2"}]}], " ", "-", " ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"4", "*", 
         RowBox[{"(", 
          RowBox[{"a3", " ", "-", " ", 
           RowBox[{"q0", "^", "2"}], " ", "+", " ", 
           RowBox[{"q1", "^", "2"}], " ", "+", " ", 
           RowBox[{"q2", "^", "2"}], " ", "-", " ", 
           RowBox[{"3", "*", 
            RowBox[{"q3", "^", "2"}]}]}], ")"}]}], ")"}], "/", 
       RowBox[{"erra3", "^", "2"}]}], " ", "+", " ", "\n", "    ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"8", "*", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{"q1", "*", "r1"}], " ", "+", " ", 
             RowBox[{"q2", "*", "r2"}]}], ")"}], "^", "2"}]}], " ", "-", " ", 
         
         RowBox[{"4", "*", 
          RowBox[{"(", 
           RowBox[{"m3", " ", "+", " ", 
            RowBox[{"2", "*", "q0", "*", "q2", "*", "r1"}], " ", "-", " ", 
            RowBox[{"6", "*", "q1", "*", "q3", "*", "r1"}], " ", "-", " ", 
            RowBox[{"2", "*", "q0", "*", "q1", "*", "r2"}], " ", "-", " ", 
            RowBox[{"6", "*", "q2", "*", "q3", "*", "r2"}]}], ")"}], "*", 
          "r3"}], " ", "-", " ", "\n", "      ", 
         RowBox[{"4", "*", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", 
             RowBox[{"q0", "^", "2"}]}], " ", "+", " ", 
            RowBox[{"q1", "^", "2"}], " ", "+", " ", 
            RowBox[{"q2", "^", "2"}], " ", "-", " ", 
            RowBox[{"3", "*", 
             RowBox[{"q3", "^", "2"}]}]}], ")"}], "*", 
          RowBox[{"r3", "^", "2"}]}]}], ")"}], "/", 
       RowBox[{"errm3", "^", "2"}]}], " ", "+", " ", "\n", "    ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"1", "/", 
         RowBox[{"errm1", "^", "2"}]}], ")"}], "*", 
       RowBox[{"(", 
        RowBox[{"4", "*", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"m1", "*", "r1"}], " ", "+", " ", 
           RowBox[{"r1", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{"(", 
                RowBox[{"-", 
                 RowBox[{"q1", "^", "2"}]}], ")"}], "*", "r1"}], " ", "+", 
              " ", 
              RowBox[{
               RowBox[{"q2", "^", "2"}], "*", "r1"}], " ", "+", " ", 
              RowBox[{"3", "*", 
               RowBox[{"q3", "^", "2"}], "*", "r1"}], " ", "-", " ", 
              RowBox[{"2", "*", "q1", "*", "q2", "*", "r2"}]}], ")"}]}], " ", 
           "-", " ", "\n", "       ", 
           RowBox[{
            RowBox[{"q0", "^", "2"}], "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"r1", "^", "2"}], " ", "-", " ", 
              RowBox[{"2", "*", 
               RowBox[{"r2", "^", "2"}]}]}], ")"}]}], " ", "-", " ", 
           RowBox[{"6", "*", "q1", "*", "q3", "*", "r1", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", 
            RowBox[{"q1", "^", "2"}], "*", 
            RowBox[{"r3", "^", "2"}]}], " ", "+", " ", "\n", "       ", 
           RowBox[{"q0", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"6", "*", "q3", "*", "r1", "*", "r2"}], " ", "-", " ", 
              RowBox[{"2", "*", "q2", "*", "r1", "*", "r3"}], " ", "-", " ", 
              RowBox[{"4", "*", "q1", "*", "r2", "*", "r3"}]}], ")"}]}]}], 
          ")"}]}], ")"}]}], " ", "+", " ", "\n", "    ", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"1", "/", 
         RowBox[{"errm2", "^", "2"}]}], ")"}], "*", 
       RowBox[{"(", 
        RowBox[{"4", "*", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"r2", "*", 
            RowBox[{"(", 
             RowBox[{"m2", " ", "-", " ", 
              RowBox[{"2", "*", "q1", "*", "q2", "*", "r1"}], " ", "+", " ", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"q1", "^", "2"}], " ", "-", " ", 
                 RowBox[{"q2", "^", "2"}], " ", "+", " ", 
                 RowBox[{"3", "*", 
                  RowBox[{"q3", "^", "2"}]}]}], ")"}], "*", "r2"}]}], ")"}]}],
            " ", "+", " ", 
           RowBox[{
            RowBox[{"q0", "^", "2"}], "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", "*", 
               RowBox[{"r1", "^", "2"}]}], " ", "-", " ", 
              RowBox[{"r2", "^", "2"}]}], ")"}]}], " ", "-", " ", "\n", 
           "       ", 
           RowBox[{"6", "*", "q2", "*", "q3", "*", "r2", "*", "r3"}], " ", 
           "+", " ", 
           RowBox[{"2", "*", 
            RowBox[{"q2", "^", "2"}], "*", 
            RowBox[{"r3", "^", "2"}]}], " ", "+", " ", 
           RowBox[{"q0", "*", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{"-", "6"}], "*", "q3", "*", "r1", "*", "r2"}], " ", 
              "+", " ", 
              RowBox[{"4", "*", "q2", "*", "r1", "*", "r3"}], " ", "+", " ", 
              RowBox[{"2", "*", "q1", "*", "r2", "*", "r3"}]}], ")"}]}]}], 
          ")"}]}], ")"}]}]}], ")"}]}]}], "}"}]], "Output",
 CellChangeTimes->{{3.547921206924135*^9, 3.547921234562643*^9}, {
   3.54792128528405*^9, 3.547921314263356*^9}, 3.547921352482918*^9},
 FormatType->"InputForm"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Sqrt", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.547921141594922*^9, 3.5479211436922207`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.003636939682463266`", ",", "0.003103256519538084`", ",", 
   "0.0039197531712989045`", ",", "0.005574596255458827`"}], "}"}]], "Output",\

 CellChangeTimes->{3.547921144062104*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Sqrt", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.547920424817203*^9, 3.547920427145083*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.0032903294033293003`", ",", "0.0026648668554962443`", ",", 
   "0.0028562807463851166`", ",", "0.003216027923180077`"}], "}"}]], "Output",\

 CellChangeTimes->{3.5479204275183268`*^9, 3.547920476646812*^9, 
  3.547921102666039*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Sqrt", "[", 
   RowBox[{"2", "/", "91382"}], "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.547873774878623*^9, 3.547873777520595*^9}, {
  3.547873939165888*^9, 3.547873944500662*^9}}],

Cell[BoxData["0.004678263380440256`"], "Output",
 CellChangeTimes->{3.547873778162959*^9, 3.547873944824657*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"%", "//", "N"}]], "Input",
 CellChangeTimes->{{3.547873780471788*^9, 3.547873780960713*^9}}],

Cell[BoxData["0.000021886148256768292`"], "Output",
 CellChangeTimes->{3.5478737812242537`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"f2", "=", 
   RowBox[{"f", "/.", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"q0", "\[Rule]", "Q2"}], ",", 
      RowBox[{"q3", "\[Rule]", "Q3"}]}], "}"}]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.547872396545499*^9, 3.547872412662797*^9}, {
  3.5478725353951263`*^9, 3.547872535546412*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"f2", "=", 
   RowBox[{"f2", "/.", 
    RowBox[{"parmin", "[", 
     RowBox[{"[", "2", "]"}], "]"}]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.547872415606838*^9, 3.54787242447817*^9}}],

Cell[CellGroupData[{

Cell[BoxData["f"], "Input",
 CellChangeTimes->{{3.5478724563048277`*^9, 3.547872456427876*^9}, 
   3.547872643472639*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Norm", "[", 
   RowBox[{"Quaternion", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"a3", " ", "q0"}], "-", 
          RowBox[{"a2", " ", "q1"}], "+", 
          RowBox[{"a1", " ", "q2"}]}], ")"}]}], " ", "q3"}], "-", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", "q2"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a3", " ", "q0"}], "-", 
         RowBox[{"a2", " ", "q1"}], "+", 
         RowBox[{"a1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a3", " ", "q0"}], "-", 
         RowBox[{"a2", " ", "q1"}], "+", 
         RowBox[{"a1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a3", " ", "q0"}], "-", 
         RowBox[{"a2", " ", "q1"}], "+", 
         RowBox[{"a1", " ", "q2"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}]}], "]"}], "]"}], "+", 
  RowBox[{"Norm", "[", 
   RowBox[{"Quaternion", "[", 
    RowBox[{
     RowBox[{"7.02326367260241`*^-18", "-", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}], " ", "q3"}], "-", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{"0.07243162614004858`", "\[VeryThinSpace]", "-", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"-", "0.41975847311937364`"}], "+", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{"0.9114359269101822`", "\[VeryThinSpace]", "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}]}], "]"}], "]"}]}]], "Output",
 CellChangeTimes->{3.547872456747238*^9, 3.547872644099527*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ContourPlot", "[", 
  RowBox[{
   RowBox[{"Log", "[", "f2", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"Q2", ",", 
     RowBox[{"-", "1"}], ",", "0.8"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"Q3", ",", 
     RowBox[{"-", "0.7"}], ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.547872426967168*^9, 3.547872515020301*^9}, {
  3.547872545546423*^9, 3.547872554410405*^9}}],

Cell[BoxData[
 GraphicsBox[GraphicsComplexBox[CompressedData["
1:eJxlXQdcTt8bFxGZ2TP9zJC9JVeEiISUrMzMyMqWPSJEKSs7Rckqs552NGjv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   "], {{{}, 
     {RGBColor[
      0.32893082585665645`, 0.11915509085320572`, 0.5793323840769022], 
      EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxFWFlslkUU/fsv882X+oISoU/ExESjQGVXq+C+RMRElioFWRRwA6QtVVyB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         "]], PolygonBox[CompressedData["
1:eJwllmlsV0UUxV/b13nzj0uMMaCfjImJBLQsLWsrKrizKVC2giwKLoiALQ2S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         "]]}]}, 
     {RGBColor[0.4826914222589297, 0.38650324264096725`, 0.7954615032024122], 
      EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxNmn20lWWZxvfe797nfbfp5BKR1FGw1QwYiJYSCDiulaaoScYQqCPpAjXR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         "]], PolygonBox[CompressedData["
1:eJwll3mUj1UYx9/f+/7md+8rHXWinOKc6pBhkFB2zkGELE0SWk7HUSnKWIam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         "]]}]}, 
     {RGBColor[0.6172215676341694, 0.6133655027930197, 0.9107161128092319], 
      EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxNmXmQVsUVxb/tfa/foGJCxA1QlgGUGDUqKooratyjlrHUBEWs0hCNmiph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         "]], 
        PolygonBox[CompressedData["
1:eJwllgtolmUUx9/vsvd5P1FbQtFFi8rNvNYkNs2mTp2WYpoixgqqKRhGCoG5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         "]]}]}, 
     {RGBColor[0.7302711849446802, 0.7950047814204125, 0.9132932958863313], 
      EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxFmHtslncVx5/27fs8zzsuAxwXQWpMaUuhLaUtCDqgbMThNEAZcrGUAiOZ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         "]], PolygonBox[CompressedData["
1:eJwtlUtslVUUhU/vvf3PuWBBKCgKiSGlUkwLKAXRKJSBvGKiFAKUV3k4gShF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         "]]}]}, 
     {RGBColor[0.8350959189281688, 0.8711631195664017, 0.8815667812583585], 
      EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxNmGuUVmUVx887877vOSdzaIRxkIsIftIvrSyX1FqmaMyggHLV0tYyLgPK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         "]], PolygonBox[CompressedData["
1:eJwtldlvjVEUxc8d+p3vIuag1ZZ640UI6ZOxrWrrFi2CGhvtbW/rNmKIBw+G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         "]]}]}, 
     {RGBColor[0.9366221480712037, 0.905019411723428, 0.8360831215832454], 
      EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJw1lbtTVVcUxveVc+45tzAoNEqUcCmNVv4FXqJmjEqijXQJo4AvtLTTSYqY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         "]], PolygonBox[CompressedData["
1:eJwlkrtOVGEUhTfM4fxnGgOxAIbLMMMjUFiD3MIlCL4AQkYGgcHOnkJQSHgB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         "]]}]}}, {{}, 
     TagBox[
      TooltipBox[
       {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
1:eJwVzkk2Q1EQh/FrolkBkeQlL1ainzCxAiJ5aSVDxpxjZAmsAMvQJDYgGJPo
7cDvDr7zVf2r6p6bVvs7vakQQgc30yHU5kLYnQlhgEV1HvPIYQGv8jt741lz
9RvnuIpD8z1+NL9FXb+vH8c93MsyWVtd4ku3BfWEG1yQPdkZqlso6puc8IQf
zL7t/uATFdmZ2Zd6aNZQ92R9/RJS9SYfcC863qCs3+Aud/nF7TV34g3WsYY2
ns2uuBXvsIqV+F80kaGOUsR7y/EdLvtLBSkS/bu8yB888OafOsO2+QVv8Tn/
4sTOyM6p7FidIC+v40hW438ZjTaG
         "]]},
       "2"],
      Annotation[#, 2, "Tooltip"]& ], 
     TagBox[
      TooltipBox[
       {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
1:eJwVzksrhGEYxvFnymlSmDEzbH0Qh40SylmGGcPYWZAc9oryWSxmoaTkTFiK
zBDCOGx9Bb938e9/X9d9P29vR3F5dCkWQlhBqS6ESkMITyijsT6EZ+7lV27i
F27mN+7jeFwX7TGAFbmf73xrD1l5UE5gGKvyEN/b7SMnj8hJjGNNHuMHuwPk
5Qn5A+841BV0k+ZbtJpTaEESCXzqj919+sdU9JZbOYt1+yl+tD/CnDwtp5HD
hjzDZbsTzMt5+QtVnOsWdAVzhnd9+wtVpOWK/RmK5lk3P/jGle7XTXuUuS3a
8aW+hzNyJ3djy9su3uYL+03zKV+7qTXXYMcc4z/9oruSfIN/3Yw98w==
         "]]},
       "1"],
      Annotation[#, 1, "Tooltip"]& ], 
     TagBox[
      TooltipBox[
       {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
1:eJwV0Lsvw1EYBuDD0JvbYMIkZve7RKJ/ghoMkqKsSiwGi82dxEjC4LaQGITS
iZVuEhMbk0jM6vJ0ePJ+3znv+TVpY2Y2lS0LIWQpRkIoj4XwIx/lA8l4CEOc
R0MYYNP8637QHCHKn31HLuqP0GxOyRaZZK70Dfmp1ypHOXSftxdlm/1btssE
af2cuydi9hl7XL7Zl+W7XJAN3tyYX82VOlVUUEM1TUzpTFNHPVf6L/rj5gnS
ZJhkng02WWebLXb19xjzvUvvh5310Es3/fSxQoIPnby85cy7ey6cFThydkwH
XXSS45qC3pdOrfnOfMCS39wv/dfOopyaV+WJXJPP8h//6Div
         "]], 
        LineBox[{2008, 2027, 2006, 2121, 2122, 2120, 1827, 1830, 2414, 1829, 
         1757, 1912, 2426, 1913, 2043, 2042, 2087, 2086}]},
       "0"],
      Annotation[#, 0, "Tooltip"]& ], 
     TagBox[
      TooltipBox[
       {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
1:eJwV0jtIlmEYBuDXAq0oFEFwqCHI8pRgg1hZQZ5IzcylaHSLQKEl8ZylFS01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         "]]},
       RowBox[{"-", "1"}]],
      Annotation[#, -1, "Tooltip"]& ], 
     TagBox[
      TooltipBox[
       {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
1:eJwl009Mz3Ecx/FPkfpNjM0429pYoVLkT+PiwEG2VP7l0qlDU+nPxuZgXKRS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         "]]},
       RowBox[{"-", "2"}]],
      Annotation[#, -2, "Tooltip"]& ], {}, {}, {}}}],
  AspectRatio->1,
  Frame->True,
  PlotRange->{{-1, 0.8}, {-0.7, 1}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{{3.547872452204363*^9, 3.547872557310598*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Conjugate", "[", "avg", "]"}], "**", "avga", "**", 
  "avg"}]], "Input",
 CellChangeTimes->{{3.5478692729272757`*^9, 3.5478692920385637`*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"3.469446951953614`*^-18", ",", 
   RowBox[{"-", "0.00037614815561166914`"}], ",", "0.0002352700112477177`", 
   ",", "0.9999999015802886`"}], "]"}]], "Output",
 CellChangeTimes->{
  3.547868695825583*^9, 3.547868762648193*^9, 3.5478688284177103`*^9, {
   3.547869185782096*^9, 3.547869233142928*^9}, 3.547869293389556*^9, {
   3.547869323544736*^9, 3.5478693457859077`*^9}, 3.547869413709074*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"QuatToEuler", "[", "Qu_", "]"}], "=", 
   RowBox[{"Hold", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"ArcTan", "[", 
       RowBox[{"2", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            RowBox[{"Qu", "[", 
             RowBox[{"[", "1", "]"}], "]"}], 
            RowBox[{"Qu", "[", 
             RowBox[{"[", "2", "]"}], "]"}]}], "-", 
           RowBox[{
            RowBox[{"Qu", "[", 
             RowBox[{"[", "3", "]"}], "]"}], 
            RowBox[{"Qu", "[", 
             RowBox[{"[", "4", "]"}], "]"}]}]}], ")"}], "/", 
         RowBox[{"(", 
          RowBox[{"1", "-", 
           RowBox[{"2", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{"Qu", "[", 
                RowBox[{"[", "2", "]"}], "]"}], "^", "2"}], "+", 
              RowBox[{
               RowBox[{"Qu", "[", 
                RowBox[{"[", "3", "]"}], "]"}], "^", "2"}]}], ")"}]}]}], 
          ")"}]}]}], "]"}], ",", " ", 
      RowBox[{"ArcSin", "[", 
       RowBox[{"2", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           RowBox[{"Qu", "[", 
            RowBox[{"[", "1", "]"}], "]"}], 
           RowBox[{"Qu", "[", 
            RowBox[{"[", "3", "]"}], "]"}]}], "+", 
          RowBox[{
           RowBox[{"Qu", "[", 
            RowBox[{"[", "4", "]"}], "]"}], 
           RowBox[{"Qu", "[", 
            RowBox[{"[", "2", "]"}], "]"}]}]}], ")"}]}], "]"}], ",", 
      RowBox[{"ArcTan", "[", 
       RowBox[{"2", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            RowBox[{"Qu", "[", 
             RowBox[{"[", "1", "]"}], "]"}], 
            RowBox[{"Qu", "[", 
             RowBox[{"[", "4", "]"}], "]"}]}], "-", 
           RowBox[{
            RowBox[{"Qu", "[", 
             RowBox[{"[", "2", "]"}], "]"}], 
            RowBox[{"Qu", "[", 
             RowBox[{"[", "3", "]"}], "]"}]}]}], ")"}], "/", 
         RowBox[{"(", 
          RowBox[{"1", "-", 
           RowBox[{"2", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{"Qu", "[", 
                RowBox[{"[", "3", "]"}], "]"}], "^", "2"}], "+", 
              RowBox[{
               RowBox[{"Qu", "[", 
                RowBox[{"[", "4", "]"}], "]"}], "^", "2"}]}], ")"}]}]}], 
          ")"}]}]}], "]"}]}], "}"}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.547868874281983*^9, 3.5478690343655663`*^9}, {
  3.547869100626514*^9, 3.547869126353305*^9}, {3.54787001325566*^9, 
  3.547870030042376*^9}}],

Cell[BoxData["{"], "Input",
 CellChangeTimes->{{3.547873546506225*^9, 3.5478735471203003`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Release", "[", 
  RowBox[{"QuatToEuler", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"q0", ",", "q1", ",", "q2", ",", "q3"}], "}"}], "/.", 
    RowBox[{"parmin", "[", 
     RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.547869053355732*^9, 3.547869072301268*^9}, {
  3.547869196451869*^9, 3.547869213502407*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1.1499320016362513`", ",", 
   RowBox[{"-", "0.33065131005050385`"}], ",", "1.4603694917826469`"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.547872338440421*^9, 3.547873445237253*^9, 
  3.547873702526805*^9, 3.547873838535149*^9, 3.547877833096101*^9, 
  3.547879001413549*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1.15284870707089`", ",", 
   RowBox[{"-", "0.33164532734813673`"}], ",", "1.4635449497273056`"}], "}"}]],\
 "Input",
 CellChangeTimes->{3.5478722654495687`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1.15284870707089`", ",", 
   RowBox[{"-", "0.33164532734813673`"}], ",", "1.4635449497273056`"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.547872265543661*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Release", "[", 
  RowBox[{"QuatToEuler", "[", "avg", "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.5478691561289387`*^9, 3.547869162660673*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1.1507164376834236`", ",", 
   RowBox[{"-", "0.3461743325839059`"}], ",", "0.000022893455811131738`"}], 
  "}"}]], "Output",
 CellChangeTimes->{
  3.5478691630625563`*^9, {3.547869242611456*^9, 3.547869246662496*^9}, 
   3.547869438443643*^9, 3.547870035174638*^9, {3.547870083020356*^9, 
   3.547870125817267*^9}, 3.547873448321067*^9, 3.547873485735326*^9, 
   3.547878996766341*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["f"], "Input",
 CellChangeTimes->{3.547870887673401*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Norm", "[", 
   RowBox[{"Quaternion", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"a3", " ", "q0"}], "-", 
          RowBox[{"a2", " ", "q1"}], "+", 
          RowBox[{"a1", " ", "q2"}]}], ")"}]}], " ", "q3"}], "-", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", "q2"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a3", " ", "q0"}], "-", 
         RowBox[{"a2", " ", "q1"}], "+", 
         RowBox[{"a1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a3", " ", "q0"}], "-", 
         RowBox[{"a2", " ", "q1"}], "+", 
         RowBox[{"a1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a3", " ", "q0"}], "-", 
         RowBox[{"a2", " ", "q1"}], "+", 
         RowBox[{"a1", " ", "q2"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a2", " ", "q0"}], "+", 
         RowBox[{"a3", " ", "q1"}], "-", 
         RowBox[{"a1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q0"}], "-", 
         RowBox[{"a3", " ", "q2"}], "+", 
         RowBox[{"a2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a1", " ", "q1"}], "+", 
         RowBox[{"a2", " ", "q2"}], "+", 
         RowBox[{"a3", " ", "q3"}]}], ")"}]}]}]}], "]"}], "]"}], "+", 
  RowBox[{"Norm", "[", 
   RowBox[{"Quaternion", "[", 
    RowBox[{
     RowBox[{"7.02326367260241`*^-18", "-", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}], " ", "q3"}], "-", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{"0.07243162614004858`", "\[VeryThinSpace]", "-", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"-", "0.41975847311937364`"}], "+", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}]}], "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "-", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}], ",", 
     RowBox[{"0.9114359269101822`", "\[VeryThinSpace]", "+", 
      RowBox[{"q0", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m3", " ", "q0"}], "-", 
         RowBox[{"m2", " ", "q1"}], "+", 
         RowBox[{"m1", " ", "q2"}]}], ")"}]}], "-", 
      RowBox[{"q1", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m2", " ", "q0"}], "+", 
         RowBox[{"m3", " ", "q1"}], "-", 
         RowBox[{"m1", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q0"}], "-", 
         RowBox[{"m3", " ", "q2"}], "+", 
         RowBox[{"m2", " ", "q3"}]}], ")"}]}], "+", 
      RowBox[{"q3", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"m1", " ", "q1"}], "+", 
         RowBox[{"m2", " ", "q2"}], "+", 
         RowBox[{"m3", " ", "q3"}]}], ")"}]}]}]}], "]"}], "]"}]}]], "Output",
 CellChangeTimes->{3.547870888121653*^9, 3.547871329172015*^9, 
  3.547871359999954*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"refm", "=", 
   RowBox[{"refm", "/", 
    RowBox[{"Norm", "[", "refm", "]"}]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.5478687343952427`*^9, 3.547868753755588*^9}}],

Cell[CellGroupData[{

Cell[BoxData["mr"], "Input",
 CellChangeTimes->{{3.547868708136025*^9, 3.547868709230268*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8201`", ",", "0.5451`", ",", 
     RowBox[{"-", "0.1446`"}], ",", 
     RowBox[{"-", "0.0961`"}], ",", "0.6648`", ",", "0.6552`", ",", 
     RowBox[{"-", "0.2641`"}], ",", "0.2425`", ",", "0.8247`", ",", "0.5371`",
      ",", 
     RowBox[{"-", "0.1365`"}], ",", 
     RowBox[{"-", "0.1129`"}], ",", 
     RowBox[{"-", "0.0133`"}], ",", "0.0999`", ",", 
     RowBox[{"-", "0.1789`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8271`", ",", "0.5376`", ",", 
     RowBox[{"-", "0.1371`"}], ",", 
     RowBox[{"-", "0.0891`"}], ",", "0.6739`", ",", "0.6573`", ",", 
     RowBox[{"-", "0.2381`"}], ",", "0.2387`", ",", "0.826`", ",", "0.5404`", 
     ",", 
     RowBox[{"-", "0.1155`"}], ",", 
     RowBox[{"-", "0.111`"}], ",", 
     RowBox[{"-", "0.0137`"}], ",", "0.1001`", ",", 
     RowBox[{"-", "0.1735`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8239`", ",", "0.54`", ",", 
     RowBox[{"-", "0.1433`"}], ",", 
     RowBox[{"-", "0.0939`"}], ",", "0.6831`", ",", "0.6573`", ",", 
     RowBox[{"-", "0.2158`"}], ",", "0.2336`", ",", "0.8262`", ",", "0.5422`",
      ",", 
     RowBox[{"-", "0.1047`"}], ",", 
     RowBox[{"-", "0.1115`"}], ",", 
     RowBox[{"-", "0.0128`"}], ",", "0.0979`", ",", 
     RowBox[{"-", "0.1674`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8321`", ",", "0.5255`", ",", 
     RowBox[{"-", "0.1494`"}], ",", 
     RowBox[{"-", "0.0943`"}], ",", "0.6903`", ",", "0.6589`", ",", 
     RowBox[{"-", "0.1941`"}], ",", "0.2271`", ",", "0.8299`", ",", "0.5373`",
      ",", 
     RowBox[{"-", "0.0998`"}], ",", 
     RowBox[{"-", "0.1122`"}], ",", 
     RowBox[{"-", "0.0156`"}], ",", "0.0947`", ",", 
     RowBox[{"-", "0.1593`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8282`", ",", "0.532`", ",", 
     RowBox[{"-", "0.1481`"}], ",", 
     RowBox[{"-", "0.0951`"}], ",", "0.6976`", ",", "0.6587`", ",", 
     RowBox[{"-", "0.1739`"}], ",", "0.2217`", ",", "0.8303`", ",", "0.5371`",
      ",", 
     RowBox[{"-", "0.0968`"}], ",", 
     RowBox[{"-", "0.1126`"}], ",", 
     RowBox[{"-", "0.0153`"}], ",", "0.0911`", ",", 
     RowBox[{"-", "0.1518`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8276`", ",", "0.5328`", ",", 
     RowBox[{"-", "0.1481`"}], ",", 
     RowBox[{"-", "0.0954`"}], ",", "0.7044`", ",", "0.658`", ",", 
     RowBox[{"-", "0.1546`"}], ",", "0.2162`", ",", "0.8304`", ",", "0.5372`",
      ",", 
     RowBox[{"-", "0.0955`"}], ",", 
     RowBox[{"-", "0.1128`"}], ",", 
     RowBox[{"-", "0.0146`"}], ",", "0.0873`", ",", 
     RowBox[{"-", "0.1442`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8295`", ",", "0.5315`", ",", 
     RowBox[{"-", "0.1438`"}], ",", 
     RowBox[{"-", "0.0921`"}], ",", "0.7107`", ",", "0.6579`", ",", 
     RowBox[{"-", "0.1352`"}], ",", "0.2091`", ",", "0.8309`", ",", "0.5368`",
      ",", 
     RowBox[{"-", "0.0928`"}], ",", 
     RowBox[{"-", "0.1131`"}], ",", 
     RowBox[{"-", "0.0144`"}], ",", "0.0844`", ",", 
     RowBox[{"-", "0.1365`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8292`", ",", "0.5329`", ",", 
     RowBox[{"-", "0.1415`"}], ",", 
     RowBox[{"-", "0.0909`"}], ",", "0.7168`", ",", "0.6566`", ",", 
     RowBox[{"-", "0.1166`"}], ",", "0.2035`", ",", "0.8314`", ",", "0.5368`",
      ",", 
     RowBox[{"-", "0.0904`"}], ",", 
     RowBox[{"-", "0.1118`"}], ",", 
     RowBox[{"-", "0.0138`"}], ",", "0.0815`", ",", 
     RowBox[{"-", "0.129`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8262`", ",", "0.537`", ",", 
     RowBox[{"-", "0.1425`"}], ",", 
     RowBox[{"-", "0.0926`"}], ",", "0.7224`", ",", "0.6548`", ",", 
     RowBox[{"-", "0.0995`"}], ",", "0.1983`", ",", "0.8302`", ",", "0.5387`",
      ",", 
     RowBox[{"-", "0.0905`"}], ",", 
     RowBox[{"-", "0.1112`"}], ",", 
     RowBox[{"-", "0.0119`"}], ",", "0.0781`", ",", 
     RowBox[{"-", "0.1218`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8269`", ",", "0.5348`", ",", 
     RowBox[{"-", "0.1458`"}], ",", 
     RowBox[{"-", "0.0943`"}], ",", "0.7269`", ",", "0.6535`", ",", 
     RowBox[{"-", "0.0828`"}], ",", "0.1938`", ",", "0.8298`", ",", "0.539`", 
     ",", 
     RowBox[{"-", "0.0926`"}], ",", 
     RowBox[{"-", "0.1106`"}], ",", 
     RowBox[{"-", "0.011`"}], ",", "0.0741`", ",", 
     RowBox[{"-", "0.1146`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8294`", ",", "0.5318`", ",", 
     RowBox[{"-", "0.1439`"}], ",", 
     RowBox[{"-", "0.0922`"}], ",", "0.7306`", ",", "0.6527`", ",", 
     RowBox[{"-", "0.0668`"}], ",", "0.1887`", ",", "0.8305`", ",", "0.538`", 
     ",", 
     RowBox[{"-", "0.0938`"}], ",", 
     RowBox[{"-", "0.1097`"}], ",", 
     RowBox[{"-", "0.0112`"}], ",", "0.0707`", ",", 
     RowBox[{"-", "0.1075`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8254`", ",", "0.5382`", ",", 
     RowBox[{"-", "0.1422`"}], ",", 
     RowBox[{"-", "0.0927`"}], ",", "0.7347`", ",", "0.6504`", ",", 
     RowBox[{"-", "0.0519`"}], ",", "0.1853`", ",", "0.8294`", ",", "0.5398`",
      ",", 
     RowBox[{"-", "0.0947`"}], ",", 
     RowBox[{"-", "0.1085`"}], ",", 
     RowBox[{"-", "0.0095`"}], ",", "0.0673`", ",", 
     RowBox[{"-", "0.1014`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8261`", ",", "0.538`", ",", 
     RowBox[{"-", "0.1402`"}], ",", 
     RowBox[{"-", "0.0913`"}], ",", "0.7377`", ",", "0.649`", ",", 
     RowBox[{"-", "0.0375`"}], ",", "0.1818`", ",", "0.8287`", ",", "0.541`", 
     ",", 
     RowBox[{"-", "0.0953`"}], ",", 
     RowBox[{"-", "0.107`"}], ",", 
     RowBox[{"-", "0.0085`"}], ",", "0.0643`", ",", 
     RowBox[{"-", "0.0954`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8245`", ",", "0.5387`", ",", 
     RowBox[{"-", "0.1445`"}], ",", 
     RowBox[{"-", "0.0944`"}], ",", "0.7403`", ",", "0.6475`", ",", 
     RowBox[{"-", "0.0238`"}], ",", "0.1785`", ",", "0.8277`", ",", "0.5421`",
      ",", 
     RowBox[{"-", "0.0984`"}], ",", 
     RowBox[{"-", "0.1068`"}], ",", 
     RowBox[{"-", "0.0075`"}], ",", "0.0605`", ",", 
     RowBox[{"-", "0.0897`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8258`", ",", "0.5347`", ",", 
     RowBox[{"-", "0.1499`"}], ",", 
     RowBox[{"-", "0.0971`"}], ",", "0.7429`", ",", "0.646`", ",", 
     RowBox[{"-", "0.0112`"}], ",", "0.1747`", ",", "0.8278`", ",", "0.5407`",
      ",", 
     RowBox[{"-", "0.1035`"}], ",", 
     RowBox[{"-", "0.1076`"}], ",", 
     RowBox[{"-", "0.0075`"}], ",", "0.0562`", ",", 
     RowBox[{"-", "0.0838`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8241`", ",", "0.5389`", ",", 
     RowBox[{"-", "0.1457`"}], ",", 
     RowBox[{"-", "0.0953`"}], ",", "0.7454`", ",", "0.6442`", ",", "0.`", 
     ",", "0.1708`", ",", "0.827`", ",", "0.5415`", ",", 
     RowBox[{"-", "0.1063`"}], ",", 
     RowBox[{"-", "0.1076`"}], ",", 
     RowBox[{"-", "0.0065`"}], ",", "0.0531`", ",", 
     RowBox[{"-", "0.0786`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8256`", ",", "0.537`", ",", 
     RowBox[{"-", "0.1448`"}], ",", 
     RowBox[{"-", "0.0942`"}], ",", "0.7473`", ",", "0.643`", ",", "0.0119`", 
     ",", "0.1668`", ",", "0.827`", ",", "0.5413`", ",", 
     RowBox[{"-", "0.1076`"}], ",", 
     RowBox[{"-", "0.1071`"}], ",", 
     RowBox[{"-", "0.0064`"}], ",", "0.0505`", ",", 
     RowBox[{"-", "0.0734`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8284`", ",", "0.5349`", ",", 
     RowBox[{"-", "0.139`"}], ",", 
     RowBox[{"-", "0.0897`"}], ",", "0.7493`", ",", "0.6412`", ",", "0.0228`",
      ",", "0.1637`", ",", "0.8284`", ",", "0.5397`", ",", 
     RowBox[{"-", "0.1067`"}], ",", 
     RowBox[{"-", "0.1047`"}], ",", 
     RowBox[{"-", "0.0069`"}], ",", "0.0488`", ",", 
     RowBox[{"-", "0.0686`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8261`", ",", "0.5341`", ",", 
     RowBox[{"-", "0.1505`"}], ",", 
     RowBox[{"-", "0.0973`"}], ",", "0.7507`", ",", "0.6395`", ",", "0.0323`",
      ",", "0.162`", ",", "0.8283`", ",", "0.5388`", ",", 
     RowBox[{"-", "0.1121`"}], ",", 
     RowBox[{"-", "0.1047`"}], ",", 
     RowBox[{"-", "0.0067`"}], ",", "0.0449`", ",", 
     RowBox[{"-", "0.064`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8218`", ",", "0.5395`", ",", 
     RowBox[{"-", "0.1527`"}], ",", 
     RowBox[{"-", "0.1002`"}], ",", "0.7516`", ",", "0.6386`", ",", "0.0421`",
      ",", "0.1594`", ",", "0.8259`", ",", "0.5412`", ",", 
     RowBox[{"-", "0.117`"}], ",", 
     RowBox[{"-", "0.1063`"}], ",", 
     RowBox[{"-", "0.0052`"}], ",", "0.0411`", ",", 
     RowBox[{"-", "0.06`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8257`", ",", "0.5372`", ",", 
     RowBox[{"-", "0.1437`"}], ",", 
     RowBox[{"-", "0.0934`"}], ",", "0.7526`", ",", "0.6374`", ",", "0.0517`",
      ",", "0.1564`", ",", "0.8263`", ",", "0.541`", ",", 
     RowBox[{"-", "0.1166`"}], ",", 
     RowBox[{"-", "0.105`"}], ",", 
     RowBox[{"-", "0.0054`"}], ",", "0.0394`", ",", 
     RowBox[{"-", "0.056`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8256`", ",", "0.5362`", ",", 
     RowBox[{"-", "0.1469`"}], ",", 
     RowBox[{"-", "0.0954`"}], ",", "0.7537`", ",", "0.6359`", ",", "0.0604`",
      ",", "0.1542`", ",", "0.8266`", ",", "0.5402`", ",", 
     RowBox[{"-", "0.1182`"}], ",", 
     RowBox[{"-", "0.1043`"}], ",", 
     RowBox[{"-", "0.0055`"}], ",", "0.0371`", ",", 
     RowBox[{"-", "0.0521`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8305`", ",", "0.5319`", ",", 
     RowBox[{"-", "0.1388`"}], ",", 
     RowBox[{"-", "0.0889`"}], ",", "0.7546`", ",", "0.6344`", ",", "0.069`", 
     ",", "0.1521`", ",", "0.829`", ",", "0.5375`", ",", 
     RowBox[{"-", "0.1164`"}], ",", 
     RowBox[{"-", "0.1014`"}], ",", 
     RowBox[{"-", "0.0068`"}], ",", "0.0362`", ",", 
     RowBox[{"-", "0.0483`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8276`", ",", "0.5347`", ",", 
     RowBox[{"-", "0.1431`"}], ",", 
     RowBox[{"-", "0.0924`"}], ",", "0.756`", ",", "0.6323`", ",", "0.0764`", 
     ",", "0.1503`", ",", "0.8292`", ",", "0.5371`", ",", 
     RowBox[{"-", "0.1176`"}], ",", 
     RowBox[{"-", "0.1007`"}], ",", 
     RowBox[{"-", "0.0064`"}], ",", "0.0342`", ",", 
     RowBox[{"-", "0.045`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8292`", ",", "0.5316`", ",", 
     RowBox[{"-", "0.145`"}], ",", 
     RowBox[{"-", "0.0929`"}], ",", "0.7566`", ",", "0.631`", ",", "0.0843`", 
     ",", "0.1485`", ",", "0.8298`", ",", "0.5359`", ",", 
     RowBox[{"-", "0.119`"}], ",", 
     RowBox[{"-", "0.1001`"}], ",", 
     RowBox[{"-", "0.0068`"}], ",", "0.0321`", ",", 
     RowBox[{"-", "0.0416`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.822`", ",", "0.5418`", ",", 
     RowBox[{"-", "0.146`"}], ",", 
     RowBox[{"-", "0.0962`"}], ",", "0.7573`", ",", "0.6295`", ",", "0.091`", 
     ",", "0.1474`", ",", "0.8269`", ",", "0.5398`", ",", 
     RowBox[{"-", "0.1215`"}], ",", 
     RowBox[{"-", "0.1007`"}], ",", 
     RowBox[{"-", "0.0044`"}], ",", "0.0295`", ",", 
     RowBox[{"-", "0.0393`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8252`", ",", "0.5369`", ",", 
     RowBox[{"-", "0.1467`"}], ",", 
     RowBox[{"-", "0.0955`"}], ",", "0.7577`", ",", "0.6282`", ",", "0.0981`",
      ",", "0.1464`", ",", "0.8267`", ",", "0.5397`", ",", 
     RowBox[{"-", "0.1232`"}], ",", 
     RowBox[{"-", "0.1006`"}], ",", 
     RowBox[{"-", "0.0043`"}], ",", "0.0273`", ",", 
     RowBox[{"-", "0.0366`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8274`", ",", "0.5338`", ",", 
     RowBox[{"-", "0.1463`"}], ",", 
     RowBox[{"-", "0.0944`"}], ",", "0.7577`", ",", "0.6274`", ",", "0.1043`",
      ",", "0.146`", ",", "0.8275`", ",", "0.5383`", ",", 
     RowBox[{"-", "0.1247`"}], ",", 
     RowBox[{"-", "0.0994`"}], ",", 
     RowBox[{"-", "0.005`"}], ",", "0.0253`", ",", 
     RowBox[{"-", "0.0339`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.826`", ",", "0.537`", ",", 
     RowBox[{"-", "0.1433`"}], ",", 
     RowBox[{"-", "0.0932`"}], ",", "0.7578`", ",", "0.6264`", ",", "0.1101`",
      ",", "0.1449`", ",", "0.8272`", ",", "0.5388`", ",", 
     RowBox[{"-", "0.1252`"}], ",", 
     RowBox[{"-", "0.0988`"}], ",", 
     RowBox[{"-", "0.0047`"}], ",", "0.0238`", ",", 
     RowBox[{"-", "0.0316`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8262`", ",", "0.5359`", ",", 
     RowBox[{"-", "0.1456`"}], ",", 
     RowBox[{"-", "0.0945`"}], ",", "0.7582`", ",", "0.6253`", ",", "0.1157`",
      ",", "0.1435`", ",", "0.8272`", ",", "0.5384`", ",", 
     RowBox[{"-", "0.1266`"}], ",", 
     RowBox[{"-", "0.099`"}], ",", 
     RowBox[{"-", "0.0047`"}], ",", "0.0221`", ",", 
     RowBox[{"-", "0.0293`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8295`", ",", "0.5313`", ",", 
     RowBox[{"-", "0.1446`"}], ",", 
     RowBox[{"-", "0.0926`"}], ",", "0.7586`", ",", "0.6241`", ",", "0.1208`",
      ",", "0.1424`", ",", "0.8288`", ",", "0.5359`", ",", 
     RowBox[{"-", "0.1274`"}], ",", 
     RowBox[{"-", "0.0982`"}], ",", 
     RowBox[{"-", "0.0057`"}], ",", "0.0208`", ",", 
     RowBox[{"-", "0.0269`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8263`", ",", "0.5355`", ",", 
     RowBox[{"-", "0.1462`"}], ",", 
     RowBox[{"-", "0.0948`"}], ",", "0.7586`", ",", "0.6232`", ",", "0.1262`",
      ",", "0.1413`", ",", "0.828`", ",", "0.5368`", ",", 
     RowBox[{"-", "0.1286`"}], ",", 
     RowBox[{"-", "0.0984`"}], ",", 
     RowBox[{"-", "0.0052`"}], ",", "0.019`", ",", 
     RowBox[{"-", "0.025`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8293`", ",", "0.5319`", ",", 
     RowBox[{"-", "0.1439`"}], ",", 
     RowBox[{"-", "0.0923`"}], ",", "0.7587`", ",", "0.6222`", ",", "0.1309`",
      ",", "0.1412`", ",", "0.8291`", ",", "0.5353`", ",", 
     RowBox[{"-", "0.1289`"}], ",", 
     RowBox[{"-", "0.097`"}], ",", 
     RowBox[{"-", "0.0059`"}], ",", "0.0179`", ",", 
     RowBox[{"-", "0.0229`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8299`", ",", "0.5302`", ",", 
     RowBox[{"-", "0.146`"}], ",", 
     RowBox[{"-", "0.0932`"}], ",", "0.759`", ",", "0.6213`", ",", "0.1354`", 
     ",", "0.1396`", ",", "0.8299`", ",", "0.5338`", ",", 
     RowBox[{"-", "0.1301`"}], ",", 
     RowBox[{"-", "0.0973`"}], ",", 
     RowBox[{"-", "0.0065`"}], ",", "0.0165`", ",", 
     RowBox[{"-", "0.0209`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8239`", ",", "0.5405`", ",", 
     RowBox[{"-", "0.142`"}], ",", 
     RowBox[{"-", "0.0932`"}], ",", "0.7595`", ",", "0.6199`", ",", "0.1393`",
      ",", "0.1389`", ",", "0.8276`", ",", "0.5373`", ",", 
     RowBox[{"-", "0.1302`"}], ",", 
     RowBox[{"-", "0.0971`"}], ",", 
     RowBox[{"-", "0.0044`"}], ",", "0.0155`", ",", 
     RowBox[{"-", "0.0197`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8264`", ",", "0.5357`", ",", 
     RowBox[{"-", "0.145`"}], ",", 
     RowBox[{"-", "0.094`"}], ",", "0.7599`", ",", "0.6191`", ",", "0.1426`", 
     ",", "0.1371`", ",", "0.8273`", ",", "0.5373`", ",", 
     RowBox[{"-", "0.1317`"}], ",", 
     RowBox[{"-", "0.0977`"}], ",", 
     RowBox[{"-", "0.0043`"}], ",", "0.0143`", ",", 
     RowBox[{"-", "0.0181`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8241`", ",", "0.5408`", ",", 
     RowBox[{"-", "0.1406`"}], ",", 
     RowBox[{"-", "0.0923`"}], ",", "0.7606`", ",", "0.6176`", ",", "0.1459`",
      ",", "0.1363`", ",", "0.8263`", ",", "0.5391`", ",", 
     RowBox[{"-", "0.1314`"}], ",", 
     RowBox[{"-", "0.097`"}], ",", 
     RowBox[{"-", "0.0029`"}], ",", "0.0138`", ",", 
     RowBox[{"-", "0.0168`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8251`", ",", "0.537`", ",", 
     RowBox[{"-", "0.1468`"}], ",", 
     RowBox[{"-", "0.0955`"}], ",", "0.7609`", ",", "0.6167`", ",", "0.1485`",
      ",", "0.136`", ",", "0.8262`", ",", "0.5385`", ",", 
     RowBox[{"-", "0.1336`"}], ",", 
     RowBox[{"-", "0.0972`"}], ",", 
     RowBox[{"-", "0.0028`"}], ",", "0.0123`", ",", 
     RowBox[{"-", "0.0155`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8313`", ",", "0.5297`", ",", 
     RowBox[{"-", "0.1416`"}], ",", 
     RowBox[{"-", "0.0902`"}], ",", "0.7606`", ",", "0.6164`", ",", "0.1517`",
      ",", "0.1352`", ",", "0.8288`", ",", "0.5351`", ",", 
     RowBox[{"-", "0.1331`"}], ",", 
     RowBox[{"-", "0.0955`"}], ",", 
     RowBox[{"-", "0.0047`"}], ",", "0.012`", ",", 
     RowBox[{"-", "0.0137`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8276`", ",", "0.5339`", ",", 
     RowBox[{"-", "0.1452`"}], ",", 
     RowBox[{"-", "0.0936`"}], ",", "0.7609`", ",", "0.6155`", ",", "0.1549`",
      ",", "0.1343`", ",", "0.8286`", ",", "0.5351`", ",", 
     RowBox[{"-", "0.134`"}], ",", 
     RowBox[{"-", "0.0959`"}], ",", 
     RowBox[{"-", "0.0045`"}], ",", "0.0109`", ",", 
     RowBox[{"-", "0.0124`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8285`", ",", "0.5313`", ",", 
     RowBox[{"-", "0.1488`"}], ",", 
     RowBox[{"-", "0.0954`"}], ",", "0.7611`", ",", "0.6147`", ",", "0.1578`",
      ",", "0.1334`", ",", "0.8289`", ",", "0.5339`", ",", 
     RowBox[{"-", "0.1359`"}], ",", 
     RowBox[{"-", "0.0969`"}], ",", 
     RowBox[{"-", "0.0049`"}], ",", "0.0095`", ",", 
     RowBox[{"-", "0.0111`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8249`", ",", "0.5367`", ",", 
     RowBox[{"-", "0.1485`"}], ",", 
     RowBox[{"-", "0.0966`"}], ",", "0.7616`", ",", "0.6139`", ",", "0.16`", 
     ",", "0.132`", ",", "0.8273`", ",", "0.5356`", ",", 
     RowBox[{"-", "0.1379`"}], ",", 
     RowBox[{"-", "0.0982`"}], ",", 
     RowBox[{"-", "0.0037`"}], ",", "0.0083`", ",", 
     RowBox[{"-", "0.0102`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.827`", ",", "0.5364`", ",", 
     RowBox[{"-", "0.1408`"}], ",", 
     RowBox[{"-", "0.0913`"}], ",", "0.7619`", ",", "0.6132`", ",", "0.162`", 
     ",", "0.1308`", ",", "0.8273`", ",", "0.5361`", ",", 
     RowBox[{"-", "0.1369`"}], ",", 
     RowBox[{"-", "0.0968`"}], ",", 
     RowBox[{"-", "0.0034`"}], ",", "0.0085`", ",", 
     RowBox[{"-", "0.009`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8259`", ",", "0.5363`", ",", 
     RowBox[{"-", "0.1458`"}], ",", 
     RowBox[{"-", "0.0946`"}], ",", "0.7619`", ",", "0.6126`", ",", "0.1644`",
      ",", "0.1305`", ",", "0.8269`", ",", "0.5366`", ",", 
     RowBox[{"-", "0.1375`"}], ",", 
     RowBox[{"-", "0.0966`"}], ",", 
     RowBox[{"-", "0.003`"}], ",", "0.0077`", ",", 
     RowBox[{"-", "0.0081`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8257`", ",", "0.5375`", ",", 
     RowBox[{"-", "0.1433`"}], ",", 
     RowBox[{"-", "0.0932`"}], ",", "0.7622`", ",", "0.6118`", ",", "0.1659`",
      ",", "0.1303`", ",", "0.8266`", ",", "0.5371`", ",", 
     RowBox[{"-", "0.1378`"}], ",", 
     RowBox[{"-", "0.0959`"}], ",", 
     RowBox[{"-", "0.0025`"}], ",", "0.0074`", ",", 
     RowBox[{"-", "0.0073`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8253`", ",", "0.5379`", ",", 
     RowBox[{"-", "0.1435`"}], ",", 
     RowBox[{"-", "0.0935`"}], ",", "0.7625`", ",", "0.611`", ",", "0.1681`", 
     ",", "0.1297`", ",", "0.8263`", ",", "0.5377`", ",", 
     RowBox[{"-", "0.1376`"}], ",", 
     RowBox[{"-", "0.0958`"}], ",", 
     RowBox[{"-", "0.002`"}], ",", "0.0069`", ",", 
     RowBox[{"-", "0.0066`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8269`", ",", "0.5355`", ",", 
     RowBox[{"-", "0.144`"}], ",", 
     RowBox[{"-", "0.0932`"}], ",", "0.7625`", ",", "0.6107`", ",", "0.1696`",
      ",", "0.1294`", ",", "0.8267`", ",", "0.537`", ",", 
     RowBox[{"-", "0.1381`"}], ",", 
     RowBox[{"-", "0.0953`"}], ",", 
     RowBox[{"-", "0.0023`"}], ",", "0.0065`", ",", 
     RowBox[{"-", "0.0057`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8266`", ",", "0.5364`", ",", 
     RowBox[{"-", "0.1425`"}], ",", 
     RowBox[{"-", "0.0925`"}], ",", "0.7625`", ",", "0.6102`", ",", "0.1716`",
      ",", "0.1289`", ",", "0.8268`", ",", "0.537`", ",", 
     RowBox[{"-", "0.1377`"}], ",", 
     RowBox[{"-", "0.0948`"}], ",", 
     RowBox[{"-", "0.0023`"}], ",", "0.0062`", ",", 
     RowBox[{"-", "0.0049`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8269`", ",", "0.5352`", ",", 
     RowBox[{"-", "0.1445`"}], ",", 
     RowBox[{"-", "0.0935`"}], ",", "0.7627`", ",", "0.6095`", ",", "0.1737`",
      ",", "0.1283`", ",", "0.8271`", ",", "0.5365`", ",", 
     RowBox[{"-", "0.1379`"}], ",", 
     RowBox[{"-", "0.0951`"}], ",", 
     RowBox[{"-", "0.0024`"}], ",", "0.0056`", ",", 
     RowBox[{"-", "0.0042`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8237`", ",", "0.54`", ",", 
     RowBox[{"-", "0.1446`"}], ",", 
     RowBox[{"-", "0.0947`"}], ",", "0.7626`", ",", "0.6091`", ",", "0.1756`",
      ",", "0.1278`", ",", "0.8256`", ",", "0.5386`", ",", 
     RowBox[{"-", "0.1384`"}], ",", 
     RowBox[{"-", "0.0956`"}], ",", 
     RowBox[{"-", "0.0014`"}], ",", "0.0049`", ",", 
     RowBox[{"-", "0.0037`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8238`", ",", "0.5382`", ",", 
     RowBox[{"-", "0.1485`"}], ",", 
     RowBox[{"-", "0.097`"}], ",", "0.7625`", ",", "0.6088`", ",", "0.1775`", 
     ",", "0.1274`", ",", "0.825`", ",", "0.539`", ",", 
     RowBox[{"-", "0.1399`"}], ",", 
     RowBox[{"-", "0.0968`"}], ",", 
     RowBox[{"-", "0.0011`"}], ",", "0.0037`", ",", 
     RowBox[{"-", "0.0031`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8233`", ",", "0.54`", ",", 
     RowBox[{"-", "0.1458`"}], ",", 
     RowBox[{"-", "0.0957`"}], ",", "0.762`", ",", "0.609`", ",", "0.1791`", 
     ",", "0.1274`", ",", "0.8242`", ",", "0.5401`", ",", 
     RowBox[{"-", "0.1405`"}], ",", 
     RowBox[{"-", "0.0964`"}], ",", 
     RowBox[{"-", "0.0008`"}], ",", "0.0031`", ",", 
     RowBox[{"-", "0.0026`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8213`", ",", "0.543`", ",", 
     RowBox[{"-", "0.1457`"}], ",", 
     RowBox[{"-", "0.0963`"}], ",", "0.7618`", ",", "0.6089`", ",", "0.1803`",
      ",", "0.1272`", ",", "0.8229`", ",", "0.5418`", ",", 
     RowBox[{"-", "0.1411`"}], ",", 
     RowBox[{"-", "0.0967`"}], ",", "0.`", ",", "0.0026`", ",", 
     RowBox[{"-", "0.0024`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8262`", ",", "0.5368`", ",", 
     RowBox[{"-", "0.1431`"}], ",", 
     RowBox[{"-", "0.093`"}], ",", "0.7616`", ",", "0.6089`", ",", "0.1815`", 
     ",", "0.1267`", ",", "0.8245`", ",", "0.5397`", ",", 
     RowBox[{"-", "0.1406`"}], ",", 
     RowBox[{"-", "0.0957`"}], ",", 
     RowBox[{"-", "0.0012`"}], ",", "0.0027`", ",", 
     RowBox[{"-", "0.0015`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8265`", ",", "0.5361`", ",", 
     RowBox[{"-", "0.1436`"}], ",", 
     RowBox[{"-", "0.0931`"}], ",", "0.7612`", ",", "0.6089`", ",", "0.1828`",
      ",", "0.127`", ",", "0.8255`", ",", "0.5384`", ",", 
     RowBox[{"-", "0.1405`"}], ",", 
     RowBox[{"-", "0.0946`"}], ",", 
     RowBox[{"-", "0.002`"}], ",", "0.0025`", ",", 
     RowBox[{"-", "0.0009`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8262`", ",", "0.5361`", ",", 
     RowBox[{"-", "0.1447`"}], ",", 
     RowBox[{"-", "0.0939`"}], ",", "0.7605`", ",", "0.6091`", ",", "0.1847`",
      ",", "0.1279`", ",", "0.8259`", ",", "0.5379`", ",", 
     RowBox[{"-", "0.1402`"}], ",", 
     RowBox[{"-", "0.0939`"}], ",", 
     RowBox[{"-", "0.0025`"}], ",", "0.002`", ",", 
     RowBox[{"-", "0.0004`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8285`", ",", "0.5349`", ",", 
     RowBox[{"-", "0.139`"}], ",", 
     RowBox[{"-", "0.0897`"}], ",", "0.7601`", ",", "0.609`", ",", "0.186`", 
     ",", "0.1289`", ",", "0.8272`", ",", "0.5366`", ",", 
     RowBox[{"-", "0.1388`"}], ",", 
     RowBox[{"-", "0.0919`"}], ",", 
     RowBox[{"-", "0.0033`"}], ",", "0.0022`", ",", "0.0001`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\<\"r\"\>", ",", "0.8262`", ",", "0.5384`", ",", 
     RowBox[{"-", "0.1387`"}], ",", 
     RowBox[{"-", "0.0904`"}], ",", "0.7602`", ",", "0.6086`", ",", "0.1871`",
      ",", "0.1291`", ",", "0.8269`", ",", "0.5375`", ",", 
     RowBox[{"-", "0.1379`"}], ",", 
     RowBox[{"-", "0.0914`"}], ",", 
     RowBox[{"-", "0.0028`"}], ",", "0.0022`", ",", "0.0002`"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.5478687096133413`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"refa", "=", 
  RowBox[{
   RowBox[{"Conjugate", "[", "avg", "]"}], "**", "avga", "**", 
   "avg"}]}], "\[IndentingNewLine]", 
 RowBox[{"refm", "=", 
  RowBox[{
   RowBox[{"Conjugate", "[", "avg", "]"}], "**", "avgm", "**", 
   "avg"}]}]}], "Input",
 CellChangeTimes->{{3.547868350322115*^9, 3.5478684017922297`*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"3.469446951953614`*^-18", ",", 
   RowBox[{"-", "0.00037614815561166914`"}], ",", "0.0002352700112477177`", 
   ",", "0.9999999015802886`"}], "]"}]], "Output",
 CellChangeTimes->{{3.547868357373661*^9, 3.54786840230683*^9}, {
  3.547873327820285*^9, 3.547873335915843*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"refm", "=", 
  RowBox[{"Quaternion", "[", 
   RowBox[{"0.`", ",", 
    RowBox[{"-", "0.07199525469458334`"}], ",", "0.41722959697199535`", ",", 
    RowBox[{"-", "0.905944891652935`"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.5478736785145817`*^9, 3.547873680093236*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"0.`", ",", 
   RowBox[{"-", "0.07199525469458334`"}], ",", "0.41722959697199535`", ",", 
   RowBox[{"-", "0.905944891652935`"}]}], "]"}]], "Output",
 CellChangeTimes->{3.547873680501292*^9, 3.547920332110425*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"q", "[", 
  RowBox[{"[", "2", "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.5478685642139606`*^9, 3.54786857672281*^9}}],

Cell[BoxData["q1"], "Output",
 CellChangeTimes->{{3.547868569068057*^9, 3.547868576997925*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Conjugate", "[", "avg", "]"}], "**", "avga", "**", 
  "avg"}]], "Input",
 CellChangeTimes->{
  3.547873242386416*^9, {3.5478767018106728`*^9, 3.5478767097356577`*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"1.3877787807814457`*^-17", ",", "0.000171409331732153`", ",", 
   RowBox[{"-", "0.0002974155019501105`"}], ",", "0.9999999410814281`"}], 
  "]"}]], "Output",
 CellChangeTimes->{{3.5478732472725983`*^9, 3.547873259580731*^9}, 
   3.547873332185357*^9, {3.547876683172284*^9, 3.547876710109789*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["avg"], "Input",
 CellChangeTimes->{{3.547877667894685*^9, 3.547877668189261*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"0.8264620226513903`", ",", "0.536003124247001`", ",", 
   RowBox[{"-", "0.14450179959371384`"}], ",", 
   RowBox[{"-", "0.09370381970125118`"}]}], "]"}]], "Output",
 CellChangeTimes->{3.547877668484214*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["avga"], "Input",
 CellChangeTimes->{{3.547876716288553*^9, 3.547876716585565*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"0.`", ",", 
   RowBox[{"-", "0.33914031204230594`"}], ",", 
   RowBox[{"-", "0.8590660600151437`"}], ",", "0.3833919055977901`"}], 
  "]"}]], "Output",
 CellChangeTimes->{3.547876716941489*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"avg", "**", 
  RowBox[{"Quaternion", "[", 
   RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "]"}], "**", 
  RowBox[{"Conjugate", "[", "avg", "]"}]}]], "Input",
 CellChangeTimes->{{3.54787671905403*^9, 3.5478767338891277`*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"0.`", ",", 
   RowBox[{"-", "0.33930157936546984`"}], ",", 
   RowBox[{"-", "0.8588917112740105`"}], ",", "0.383639761423264`"}], 
  "]"}]], "Output",
 CellChangeTimes->{3.5478767342627077`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{"rotmatpost", "/.", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"q0", "\[Rule]", 
       RowBox[{"avg", "[", 
        RowBox[{"[", "1", "]"}], "]"}]}], ",", 
      RowBox[{"q1", "\[Rule]", 
       RowBox[{"avg", "[", 
        RowBox[{"[", "2", "]"}], "]"}]}], ",", 
      RowBox[{"q2", "\[Rule]", 
       RowBox[{"avg", "[", 
        RowBox[{"[", "3", "]"}], "]"}]}], ",", 
      RowBox[{"q3", "\[Rule]", 
       RowBox[{"avg", "[", 
        RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}]}], ")"}], ".", 
  RowBox[{"{", 
   RowBox[{"0", ",", "0", ",", "1"}], "}"}]}]], "Input",
 CellChangeTimes->{{3.547876752792035*^9, 3.5478768309779863`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "0.33930157936546984`"}], ",", 
   RowBox[{"-", "0.8588917112740105`"}], ",", "0.383639761423264`"}], 
  "}"}]], "Output",
 CellChangeTimes->{
  3.5478767626702642`*^9, {3.547876812939972*^9, 3.5478768319920073`*^9}}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
    "post", " ", "multiplying", " ", "plane", " ", "to", " ", "get", " ", 
     "earth"}], ",", " ", 
    RowBox[{"checked", ":"}]}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"which", " ", "is", " ", "also", " ", "the", " ", "pre"}], "-", 
    RowBox[{
    "multiplying", " ", "matrix", " ", "for", " ", "going", " ", "from", " ", 
     "earh", " ", "to", " ", "plane"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  
  RowBox[{
   RowBox[{
    RowBox[{"q0", "=."}], ";", 
    RowBox[{"q1", "=."}], ";", 
    RowBox[{"q2", "=."}], ";", 
    RowBox[{"q3", "=."}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"rotmatpost", "=", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{
         RowBox[{
          RowBox[{"q0", "^", "2"}], "+", 
          RowBox[{"q1", "^", "2"}], "-", 
          RowBox[{"q2", "^", "2"}], "-", 
          RowBox[{"q3", "^", "2"}]}], ",", " ", 
         RowBox[{"2", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"q1", " ", "q2"}], "-", 
            RowBox[{"q0", " ", "q3"}]}], ")"}]}], ",", " ", 
         RowBox[{"2", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"q0", " ", "q2"}], "+", 
            RowBox[{"q1", " ", "q3"}]}], ")"}]}]}], "}"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"2", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"q1", " ", "q2"}], "+", 
            RowBox[{"q0", " ", "q3"}]}], ")"}]}], ",", " ", 
         RowBox[{
          RowBox[{"q0", "^", "2"}], "-", 
          RowBox[{"q1", "^", "2"}], "+", 
          RowBox[{"q2", "^", "2"}], "-", 
          RowBox[{"q3", "^", "2"}]}], ",", " ", 
         RowBox[{"2", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"q2", " ", "q3"}], "-", 
            RowBox[{"q0", " ", "q1"}]}], ")"}]}]}], "}"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"q1", " ", "q3"}], "-", 
            RowBox[{"q0", " ", "q2"}]}], ")"}]}], ",", 
         RowBox[{"2", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"q0", " ", "q1"}], "+", 
            RowBox[{"q2", " ", "q3"}]}], ")"}]}], ",", " ", 
         RowBox[{
          RowBox[{"q0", "^", "2"}], "-", 
          RowBox[{"q1", "^", "2"}], "-", 
          RowBox[{"q2", "^", "2"}], "+", 
          RowBox[{"q3", "^", "2"}]}]}], "}"}]}], "}"}]}], ";"}]}]}]], "Input",\

 CellChangeTimes->{{3.54787579639334*^9, 3.547875860853071*^9}, {
  3.5478766691315613`*^9, 3.547876676818386*^9}, {3.5478768386163893`*^9, 
  3.547876854557455*^9}}],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.547875819034727*^9, 3.5478758393183413`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
    "premultiplying", " ", "plane", " ", "to", " ", "get", " ", "earth"}], 
    ",", " ", 
    RowBox[{"checked", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"rotmat", "=", 
   RowBox[{"Transpose", "[", "rotmatpost", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.547875800026463*^9, 3.547875845971429*^9}, {
  3.547876663988475*^9, 3.547876681066946*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      SuperscriptBox["q0", "2"], "+", 
      SuperscriptBox["q1", "2"], "-", 
      SuperscriptBox["q2", "2"], "-", 
      SuperscriptBox["q3", "2"]}], ",", 
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q1", " ", "q2"}], "+", 
        RowBox[{"q0", " ", "q3"}]}], ")"}]}], ",", 
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "q0"}], " ", "q2"}], "+", 
        RowBox[{"q1", " ", "q3"}]}], ")"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q1", " ", "q2"}], "-", 
        RowBox[{"q0", " ", "q3"}]}], ")"}]}], ",", 
     RowBox[{
      SuperscriptBox["q0", "2"], "-", 
      SuperscriptBox["q1", "2"], "+", 
      SuperscriptBox["q2", "2"], "-", 
      SuperscriptBox["q3", "2"]}], ",", 
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", " ", "q1"}], "+", 
        RowBox[{"q2", " ", "q3"}]}], ")"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", " ", "q2"}], "+", 
        RowBox[{"q1", " ", "q3"}]}], ")"}]}], ",", 
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "q0"}], " ", "q1"}], "+", 
        RowBox[{"q2", " ", "q3"}]}], ")"}]}], ",", 
     RowBox[{
      SuperscriptBox["q0", "2"], "-", 
      SuperscriptBox["q1", "2"], "-", 
      SuperscriptBox["q2", "2"], "+", 
      SuperscriptBox["q3", "2"]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.547875846359913*^9, 3.547875863736212*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.547875866165904*^9, 3.547875867834811*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       SuperscriptBox["q0", "2"], "+", 
       SuperscriptBox["q1", "2"], "-", 
       SuperscriptBox["q2", "2"], "-", 
       SuperscriptBox["q3", "2"]}], 
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"q1", " ", "q2"}], "+", 
         RowBox[{"q0", " ", "q3"}]}], ")"}]}], 
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "q0"}], " ", "q2"}], "+", 
         RowBox[{"q1", " ", "q3"}]}], ")"}]}]},
     {
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"q1", " ", "q2"}], "-", 
         RowBox[{"q0", " ", "q3"}]}], ")"}]}], 
      RowBox[{
       SuperscriptBox["q0", "2"], "-", 
       SuperscriptBox["q1", "2"], "+", 
       SuperscriptBox["q2", "2"], "-", 
       SuperscriptBox["q3", "2"]}], 
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"q0", " ", "q1"}], "+", 
         RowBox[{"q2", " ", "q3"}]}], ")"}]}]},
     {
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"q0", " ", "q2"}], "+", 
         RowBox[{"q1", " ", "q3"}]}], ")"}]}], 
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "q0"}], " ", "q1"}], "+", 
         RowBox[{"q2", " ", "q3"}]}], ")"}]}], 
      RowBox[{
       SuperscriptBox["q0", "2"], "-", 
       SuperscriptBox["q1", "2"], "-", 
       SuperscriptBox["q2", "2"], "+", 
       SuperscriptBox["q3", "2"]}]}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.547875868220579*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"M", "=", 
   RowBox[{"KroneckerProduct", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"1", ",", "0"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0", ",", "1"}], "}"}]}], "}"}], ",", "rotmatpost"}], "]"}]}],
   ";"}]], "Input",
 CellChangeTimes->{{3.547876502347342*^9, 3.547876575490782*^9}, {
  3.547876858467196*^9, 3.547876858743949*^9}, {3.5478777074769793`*^9, 
  3.54787773609265*^9}, {3.547877795380027*^9, 3.547877795841825*^9}, {
  3.547877855768077*^9, 3.547877856095188*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"avga", "[", 
  RowBox[{"[", "1", "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.547878317625016*^9, 3.547878320703081*^9}}],

Cell[BoxData["0.`"], "Output",
 CellChangeTimes->{3.547878321072856*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["refm"], "Input",
 CellChangeTimes->{{3.547878342982188*^9, 3.547878345279415*^9}}],

Cell[BoxData[
 RowBox[{"Quaternion", "[", 
  RowBox[{"0.`", ",", 
   RowBox[{"-", "0.07199525469458334`"}], ",", "0.41722959697199535`", ",", 
   RowBox[{"-", "0.905944891652935`"}]}], "]"}]], "Output",
 CellChangeTimes->{3.547878345660831*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"guess", "=", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"q0", ",", "q1", ",", "q2", ",", "q3"}], "}"}], "/.", 
   RowBox[{"parmin", "[", 
    RowBox[{"[", "2", "]"}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.547878397022376*^9, 3.547878401820711*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "0.6763419955558382`"}], ",", 
   RowBox[{"-", "0.30749670819054215`"}], ",", "0.4607080988205089`", ",", 
   RowBox[{"-", "0.4854252669876748`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.54787840212323*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"mz", "=."}], ";"}]], "Input",
 CellChangeTimes->{{3.547879428265092*^9, 3.54787942895455*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"yref", "=", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1", ",", "mrx", ",", "mry", ",", "mrz"}], 
    "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ymes", "=", 
   RowBox[{"{", 
    RowBox[{
    "max", ",", "may", ",", "maz", ",", "mmx", ",", "mmy", ",", "mmz"}], 
    "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"MatrixForm", "[", 
  RowBox[{"err", "=", 
   RowBox[{"ymes", "-", 
    RowBox[{"M", ".", "yref"}]}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.547879419436384*^9, 3.547879433669642*^9}, {
  3.547880894710135*^9, 3.5478809304513206`*^9}, {3.547881336624885*^9, 
  3.5478814094779377`*^9}}],

Cell[BoxData[
 RowBox[{"MatrixForm", "[", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"max", " ", "-", " ", 
     RowBox[{"2", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", "*", "q2"}], " ", "+", " ", 
        RowBox[{"q1", "*", "q3"}]}], ")"}]}]}], ",", " ", 
    RowBox[{"may", " ", "-", " ", 
     RowBox[{"2", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "q0"}], ")"}], "*", "q1"}], " ", "+", " ", 
        RowBox[{"q2", "*", "q3"}]}], ")"}]}]}], ",", " ", "\n", "   ", 
    RowBox[{"maz", " ", "-", " ", 
     RowBox[{"q0", "^", "2"}], " ", "+", " ", 
     RowBox[{"q1", "^", "2"}], " ", "+", " ", 
     RowBox[{"q2", "^", "2"}], " ", "-", " ", 
     RowBox[{"q3", "^", "2"}]}], ",", " ", 
    RowBox[{"mmx", " ", "-", " ", 
     RowBox[{"2", "*", "mry", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q1", "*", "q2"}], " ", "-", " ", 
        RowBox[{"q0", "*", "q3"}]}], ")"}]}], " ", "-", " ", 
     RowBox[{"2", "*", "mrz", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", "*", "q2"}], " ", "+", " ", 
        RowBox[{"q1", "*", "q3"}]}], ")"}]}], " ", "-", " ", "\n", "    ", 
     RowBox[{"mrx", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", "^", "2"}], " ", "+", " ", 
        RowBox[{"q1", "^", "2"}], " ", "-", " ", 
        RowBox[{"q2", "^", "2"}], " ", "-", " ", 
        RowBox[{"q3", "^", "2"}]}], ")"}]}]}], ",", " ", 
    RowBox[{"mmy", " ", "-", " ", 
     RowBox[{"2", "*", "mrx", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q1", "*", "q2"}], " ", "+", " ", 
        RowBox[{"q0", "*", "q3"}]}], ")"}]}], " ", "-", " ", 
     RowBox[{"2", "*", "mrz", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "q0"}], ")"}], "*", "q1"}], " ", "+", " ", 
        RowBox[{"q2", "*", "q3"}]}], ")"}]}], " ", "-", " ", "\n", "    ", 
     RowBox[{"mry", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", "^", "2"}], " ", "-", " ", 
        RowBox[{"q1", "^", "2"}], " ", "+", " ", 
        RowBox[{"q2", "^", "2"}], " ", "-", " ", 
        RowBox[{"q3", "^", "2"}]}], ")"}]}]}], ",", " ", 
    RowBox[{"mmz", " ", "-", " ", 
     RowBox[{"2", "*", "mrx", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "q0"}], ")"}], "*", "q2"}], " ", "+", " ", 
        RowBox[{"q1", "*", "q3"}]}], ")"}]}], " ", "-", " ", 
     RowBox[{"2", "*", "mry", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", "*", "q1"}], " ", "+", " ", 
        RowBox[{"q2", "*", "q3"}]}], ")"}]}], " ", "-", " ", "\n", "    ", 
     RowBox[{"mrz", "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"q0", "^", "2"}], " ", "-", " ", 
        RowBox[{"q1", "^", "2"}], " ", "-", " ", 
        RowBox[{"q2", "^", "2"}], " ", "+", " ", 
        RowBox[{"q3", "^", "2"}]}], ")"}]}]}]}], "}"}], "]"}]], "Output",
 CellChangeTimes->{{3.547880923946851*^9, 3.547880930862893*^9}, {
   3.547881341250573*^9, 3.547881365642671*^9}, {3.547881397878335*^9, 
   3.54788140990633*^9}, 3.547881538749449*^9},
 FormatType->"InputForm"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"MatrixForm", "[", 
    RowBox[{
     RowBox[{"D", "[", 
      RowBox[{"M", ",", "q0"}], "]"}], ".", "yref"}], "]"}], ",", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{
     RowBox[{"D", "[", 
      RowBox[{"M", ",", "q1"}], "]"}], ".", "yref"}], "]"}], ",", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{
     RowBox[{"D", "[", 
      RowBox[{"M", ",", "q2"}], "]"}], ".", "yref"}], "]"}], ",", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{
     RowBox[{"D", "[", 
      RowBox[{"M", ",", "q3"}], "]"}], ".", "yref"}], "]"}]}], "}"}]], "Input",\

 CellChangeTimes->{{3.547879361217032*^9, 3.547879373770496*^9}, {
  3.547879438162979*^9, 3.547879441147504*^9}, {3.54787983792761*^9, 
  3.547879855937889*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   TagBox[
    RowBox[{"(", "\[NoBreak]", 
     TagBox[GridBox[{
        {
         RowBox[{"2", " ", "q2"}]},
        {
         RowBox[{
          RowBox[{"-", "2"}], " ", "q1"}]},
        {
         RowBox[{"2", " ", "q0"}]},
        {
         RowBox[{
          RowBox[{"2", " ", "mx", " ", "q0"}], "+", 
          RowBox[{"2", " ", "mz", " ", "q2"}], "-", 
          RowBox[{"2", " ", "my", " ", "q3"}]}]},
        {
         RowBox[{
          RowBox[{"2", " ", "my", " ", "q0"}], "-", 
          RowBox[{"2", " ", "mz", " ", "q1"}], "+", 
          RowBox[{"2", " ", "mx", " ", "q3"}]}]},
        {
         RowBox[{
          RowBox[{"2", " ", "mz", " ", "q0"}], "+", 
          RowBox[{"2", " ", "my", " ", "q1"}], "-", 
          RowBox[{"2", " ", "mx", " ", "q2"}]}]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.5599999999999999]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      Column], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]], ",", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", 
     TagBox[GridBox[{
        {
         RowBox[{"2", " ", "q3"}]},
        {
         RowBox[{
          RowBox[{"-", "2"}], " ", "q0"}]},
        {
         RowBox[{
          RowBox[{"-", "2"}], " ", "q1"}]},
        {
         RowBox[{
          RowBox[{"2", " ", "mx", " ", "q1"}], "+", 
          RowBox[{"2", " ", "my", " ", "q2"}], "+", 
          RowBox[{"2", " ", "mz", " ", "q3"}]}]},
        {
         RowBox[{
          RowBox[{
           RowBox[{"-", "2"}], " ", "mz", " ", "q0"}], "-", 
          RowBox[{"2", " ", "my", " ", "q1"}], "+", 
          RowBox[{"2", " ", "mx", " ", "q2"}]}]},
        {
         RowBox[{
          RowBox[{"2", " ", "my", " ", "q0"}], "-", 
          RowBox[{"2", " ", "mz", " ", "q1"}], "+", 
          RowBox[{"2", " ", "mx", " ", "q3"}]}]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.5599999999999999]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      Column], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]], ",", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", 
     TagBox[GridBox[{
        {
         RowBox[{"2", " ", "q0"}]},
        {
         RowBox[{"2", " ", "q3"}]},
        {
         RowBox[{
          RowBox[{"-", "2"}], " ", "q2"}]},
        {
         RowBox[{
          RowBox[{"2", " ", "mz", " ", "q0"}], "+", 
          RowBox[{"2", " ", "my", " ", "q1"}], "-", 
          RowBox[{"2", " ", "mx", " ", "q2"}]}]},
        {
         RowBox[{
          RowBox[{"2", " ", "mx", " ", "q1"}], "+", 
          RowBox[{"2", " ", "my", " ", "q2"}], "+", 
          RowBox[{"2", " ", "mz", " ", "q3"}]}]},
        {
         RowBox[{
          RowBox[{
           RowBox[{"-", "2"}], " ", "mx", " ", "q0"}], "-", 
          RowBox[{"2", " ", "mz", " ", "q2"}], "+", 
          RowBox[{"2", " ", "my", " ", "q3"}]}]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.5599999999999999]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      Column], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]], ",", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", 
     TagBox[GridBox[{
        {
         RowBox[{"2", " ", "q1"}]},
        {
         RowBox[{"2", " ", "q2"}]},
        {
         RowBox[{"2", " ", "q3"}]},
        {
         RowBox[{
          RowBox[{
           RowBox[{"-", "2"}], " ", "my", " ", "q0"}], "+", 
          RowBox[{"2", " ", "mz", " ", "q1"}], "-", 
          RowBox[{"2", " ", "mx", " ", "q3"}]}]},
        {
         RowBox[{
          RowBox[{"2", " ", "mx", " ", "q0"}], "+", 
          RowBox[{"2", " ", "mz", " ", "q2"}], "-", 
          RowBox[{"2", " ", "my", " ", "q3"}]}]},
        {
         RowBox[{
          RowBox[{"2", " ", "mx", " ", "q1"}], "+", 
          RowBox[{"2", " ", "my", " ", "q2"}], "+", 
          RowBox[{"2", " ", "mz", " ", "q3"}]}]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.5599999999999999]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      Column], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}], "}"}]], "Output",
 CellChangeTimes->{{3.547879366075082*^9, 3.547879374622431*^9}, 
   3.5478794416134367`*^9, {3.5478798469048157`*^9, 3.5478798564519*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"%", "//", "Order"}]], "Input",
 CellChangeTimes->{{3.547880203522093*^9, 3.547880212360376*^9}}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"Order", "::", "argr"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"\[NoBreak]\\!\\(Order\\)\[NoBreak] called with 1 argument; \
\[NoBreak]\\!\\(2\\)\[NoBreak] arguments are expected. \
\\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \
ButtonFrame->None, ButtonData:>\\\"paclet:ref/Order\\\", ButtonNote -> \
\\\"Order::argr\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.547880212979437*^9}],

Cell[BoxData[
 RowBox[{"Order", "[", 
  RowBox[{"{", 
   RowBox[{
    TagBox[
     RowBox[{"(", "\[NoBreak]", 
      TagBox[GridBox[{
         {
          RowBox[{"2", " ", "q2"}]},
         {
          RowBox[{
           RowBox[{"-", "2"}], " ", "q1"}]},
         {
          RowBox[{"2", " ", "q0"}]},
         {
          RowBox[{
           RowBox[{"2", " ", "mx", " ", "q0"}], "+", 
           RowBox[{"2", " ", "mz", " ", "q2"}], "-", 
           RowBox[{"2", " ", "my", " ", "q3"}]}]},
         {
          RowBox[{
           RowBox[{"2", " ", "my", " ", "q0"}], "-", 
           RowBox[{"2", " ", "mz", " ", "q1"}], "+", 
           RowBox[{"2", " ", "mx", " ", "q3"}]}]},
         {
          RowBox[{
           RowBox[{"2", " ", "mz", " ", "q0"}], "+", 
           RowBox[{"2", " ", "my", " ", "q1"}], "-", 
           RowBox[{"2", " ", "mx", " ", "q2"}]}]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.5599999999999999]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       Column], "\[NoBreak]", ")"}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]], ",", 
    TagBox[
     RowBox[{"(", "\[NoBreak]", 
      TagBox[GridBox[{
         {
          RowBox[{"2", " ", "q3"}]},
         {
          RowBox[{
           RowBox[{"-", "2"}], " ", "q0"}]},
         {
          RowBox[{
           RowBox[{"-", "2"}], " ", "q1"}]},
         {
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"mx", " ", "q1"}], "+", 
             RowBox[{"my", " ", "q2"}], "+", 
             RowBox[{"mz", " ", "q3"}]}], ")"}]}]},
         {
          RowBox[{
           RowBox[{"-", "2"}], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"mz", " ", "q0"}], "+", 
             RowBox[{"my", " ", "q1"}], "-", 
             RowBox[{"mx", " ", "q2"}]}], ")"}]}]},
         {
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"my", " ", "q0"}], "-", 
             RowBox[{"mz", " ", "q1"}], "+", 
             RowBox[{"mx", " ", "q3"}]}], ")"}]}]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.5599999999999999]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       Column], "\[NoBreak]", ")"}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]], ",", 
    TagBox[
     RowBox[{"(", "\[NoBreak]", 
      TagBox[GridBox[{
         {
          RowBox[{"2", " ", "q0"}]},
         {
          RowBox[{"2", " ", "q3"}]},
         {
          RowBox[{
           RowBox[{"-", "2"}], " ", "q2"}]},
         {
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"mz", " ", "q0"}], "+", 
             RowBox[{"my", " ", "q1"}], "-", 
             RowBox[{"mx", " ", "q2"}]}], ")"}]}]},
         {
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"mx", " ", "q1"}], "+", 
             RowBox[{"my", " ", "q2"}], "+", 
             RowBox[{"mz", " ", "q3"}]}], ")"}]}]},
         {
          RowBox[{
           RowBox[{"-", "2"}], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"mx", " ", "q0"}], "+", 
             RowBox[{"mz", " ", "q2"}], "-", 
             RowBox[{"my", " ", "q3"}]}], ")"}]}]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.5599999999999999]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       Column], "\[NoBreak]", ")"}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]], ",", 
    TagBox[
     RowBox[{"(", "\[NoBreak]", 
      TagBox[GridBox[{
         {
          RowBox[{"2", " ", "q1"}]},
         {
          RowBox[{"2", " ", "q2"}]},
         {
          RowBox[{"2", " ", "q3"}]},
         {
          RowBox[{
           RowBox[{"-", "2"}], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"my", " ", "q0"}], "-", 
             RowBox[{"mz", " ", "q1"}], "+", 
             RowBox[{"mx", " ", "q3"}]}], ")"}]}]},
         {
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"mx", " ", "q0"}], "+", 
             RowBox[{"mz", " ", "q2"}], "-", 
             RowBox[{"my", " ", "q3"}]}], ")"}]}]},
         {
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"mx", " ", "q1"}], "+", 
             RowBox[{"my", " ", "q2"}], "+", 
             RowBox[{"mz", " ", "q3"}]}], ")"}]}]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.5599999999999999]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       Column], "\[NoBreak]", ")"}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]]}], "}"}], "]"}]], "Output",
 CellChangeTimes->{{3.547880205604836*^9, 3.547880212984405*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["yref"], "Input",
 CellChangeTimes->{{3.547879381769432*^9, 3.5478793821081448`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0", ",", "0", ",", "1", ",", 
   RowBox[{"-", "0.07199525469458334`"}], ",", "0.41722959697199535`", ",", 
   RowBox[{"-", "0.905944891652935`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.547879382451384*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"guess", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"guess", "=", 
   RowBox[{"{", 
    RowBox[{"0.8264620226513903`", ",", "0.536003124247001`", ",", 
     RowBox[{"-", "0.14450179959371384`"}], ",", 
     RowBox[{"-", "0.09370381970125118`"}]}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"guess", "=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"q0", ",", "q1", ",", "q2", ",", "q3"}], "}"}], "/.", 
      RowBox[{"parmin", "[", 
       RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "+", 
    RowBox[{"{", 
     RowBox[{"0.01", ",", "0.01", ",", "0.01", ",", "0.01"}], "}"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"guess", "=", 
    RowBox[{"{", 
     RowBox[{"0.5", ",", "0.5", ",", "0.5", ",", "0.5"}], "}"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"yref", "=", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1", ",", 
     RowBox[{"refm", "[", 
      RowBox[{"[", "2", "]"}], "]"}], ",", 
     RowBox[{"refm", "[", 
      RowBox[{"[", "3", "]"}], "]"}], ",", 
     RowBox[{"refm", "[", 
      RowBox[{"[", "4", "]"}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"ymes", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"avga", "[", 
       RowBox[{"[", "2", "]"}], "]"}], ",", 
      RowBox[{"avga", "[", 
       RowBox[{"[", "3", "]"}], "]"}], ",", 
      RowBox[{"avga", "[", 
       RowBox[{"[", "4", "]"}], "]"}], ",", 
      RowBox[{"avgm", "[", 
       RowBox[{"[", "2", "]"}], "]"}], ",", 
      RowBox[{"avgm", "[", 
       RowBox[{"[", "3", "]"}], "]"}], ",", 
      RowBox[{"avgm", "[", 
       RowBox[{"[", "4", "]"}], "]"}]}], "}"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"For", "[", 
   RowBox[{
    RowBox[{"i", "=", "1"}], ",", 
    RowBox[{"i", "<", "5"}], ",", 
    RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"J1", "=", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"D", "[", 
          RowBox[{"M", ",", " ", "q0"}], "]"}], ".", "yref"}], ")"}], "/.", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"q0", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"q1", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"q2", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"q3", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"J2", "=", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"D", "[", 
          RowBox[{"M", ",", " ", "q1"}], "]"}], ".", "yref"}], ")"}], "/.", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"q0", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"q1", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"q2", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"q3", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"J3", "=", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"D", "[", 
          RowBox[{"M", ",", " ", "q2"}], "]"}], ".", "yref"}], ")"}], "/.", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"q0", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"q1", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"q2", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"q3", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"J4", "=", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"D", "[", 
          RowBox[{"M", ",", " ", "q3"}], "]"}], ".", "yref"}], ")"}], "/.", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"q0", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"q1", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"q2", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"q3", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"J", "=", 
      RowBox[{"-", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"KroneckerProduct", "[", 
          RowBox[{"J1", ",", 
           RowBox[{"{", 
            RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}]}], "]"}], "+", 
         
         RowBox[{"KroneckerProduct", "[", 
          RowBox[{"J2", ",", 
           RowBox[{"{", 
            RowBox[{"0", ",", "1", ",", "0", ",", "0"}], "}"}]}], "]"}], "+", 
         
         RowBox[{"KroneckerProduct", "[", 
          RowBox[{"J3", ",", 
           RowBox[{"{", 
            RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}]}], "]"}], "+", 
         
         RowBox[{"KroneckerProduct", "[", 
          RowBox[{"J4", ",", 
           RowBox[{"{", 
            RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "}"}]}], "]"}]}], 
        ")"}]}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"err", "=", 
      RowBox[{
       RowBox[{"ymes", "-", 
        RowBox[{"M", ".", "yref"}]}], "/.", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"q0", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"q1", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"q2", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"q3", "\[Rule]", 
          RowBox[{"guess", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"Print", "[", 
      RowBox[{"J", "//", "MatrixForm"}], "]"}], ";", "\[IndentingNewLine]", 
     RowBox[{"Print", "[", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"Inverse", "[", 
         RowBox[{
          RowBox[{"Transpose", "[", "J", "]"}], ".", "J"}], "]"}], ")"}], "//",
        "MatrixForm"}], "]"}], ";", "\[IndentingNewLine]", 
     RowBox[{"Print", "[", 
      RowBox[{
       RowBox[{"Inverse", "[", 
        RowBox[{
         RowBox[{"Transpose", "[", "J", "]"}], ".", "J"}], "]"}], ".", 
       RowBox[{"Transpose", "[", "J", "]"}], ".", "err"}], "]"}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"guess", "=", 
      RowBox[{"guess", "-", 
       RowBox[{
        RowBox[{"Inverse", "[", 
         RowBox[{
          RowBox[{"Transpose", "[", "J", "]"}], ".", "J"}], "]"}], ".", 
        RowBox[{"Transpose", "[", "J", "]"}], ".", "err"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"Print", "[", "guess", "]"}], ";"}]}], "\[IndentingNewLine]", 
   "]"}], ";"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5478759445681553`*^9, 3.547876038162857*^9}, 
   3.5478764958220654`*^9, {3.547876614569633*^9, 3.547876647217972*^9}, {
   3.547876865053999*^9, 3.547876913829652*^9}, {3.547876953606221*^9, 
   3.547876981068986*^9}, {3.547877030124308*^9, 3.547877079570449*^9}, {
   3.547877184043639*^9, 3.547877184426977*^9}, {3.5478772173925753`*^9, 
   3.547877535789825*^9}, {3.547877566145509*^9, 3.547877608054407*^9}, {
   3.5478776758198957`*^9, 3.5478776820017633`*^9}, {3.5478777834302397`*^9, 
   3.547877783660172*^9}, {3.54787784210743*^9, 3.547877850282892*^9}, {
   3.547877942190281*^9, 3.547877955342795*^9}, {3.547878106260833*^9, 
   3.547878245886417*^9}, {3.5478783492568293`*^9, 3.547878371394712*^9}, {
   3.547878422466213*^9, 3.547878463036058*^9}, {3.547878513599793*^9, 
   3.5478785276843777`*^9}, {3.547878725491185*^9, 3.547878756161721*^9}, {
   3.547878836033453*^9, 3.5478788852732964`*^9}, {3.547879283167263*^9, 
   3.547879303567136*^9}, {3.5478793514723454`*^9, 3.547879358086247*^9}, {
   3.547880563650713*^9, 3.547880586463936*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"-", "1.`"}], 
      RowBox[{"-", "1.`"}], 
      RowBox[{"-", "1.`"}], 
      RowBox[{"-", "1.`"}]},
     {"1.`", "1.`", 
      RowBox[{"-", "1.`"}], 
      RowBox[{"-", "1.`"}]},
     {
      RowBox[{"-", "1.`"}], "1.`", "1.`", 
      RowBox[{"-", "1.`"}]},
     {"1.3951697433195136`", "0.560710549375523`", "0.4167200399863563`", 
      "1.2511792339303471`"},
     {
      RowBox[{"-", "1.2511792339303471`"}], 
      RowBox[{"-", "0.4167200399863563`"}], "0.560710549375523`", 
      "1.3951697433195136`"},
     {"0.4167200399863563`", 
      RowBox[{"-", "1.2511792339303471`"}], 
      RowBox[{"-", "1.3951697433195136`"}], "0.560710549375523`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588944726*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0.5312346495899368`", 
      RowBox[{"-", "0.6195835928282806`"}], "0.5827690628458936`", 
      RowBox[{"-", "0.36942011960754984`"}]},
     {
      RowBox[{"-", "0.6195835928282803`"}], "1.0793182291361774`", 
      RowBox[{"-", "0.8965579322373375`"}], "0.5618232959294405`"},
     {"0.5827690628458935`", 
      RowBox[{"-", "0.8965579322373374`"}], "0.9674119422689444`", 
      RowBox[{"-", "0.5286230728775003`"}]},
     {
      RowBox[{"-", "0.3694201196075497`"}], "0.5618232959294406`", 
      RowBox[{"-", "0.5286230728775004`"}], "0.4612198965556096`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588948625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "0.0681134948852852`"}], ",", "0.25485317484426273`", ",", 
   "0.5671344611879424`", ",", "0.48279739604068395`"}], "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.54788058895186*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.5681134948852852`", ",", "0.24514682515573727`", ",", 
   RowBox[{"-", "0.06713446118794242`"}], ",", "0.017202603959316054`"}], 
  "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.5478805889546432`*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0.13426892237588484`", 
      RowBox[{"-", "0.03440520791863211`"}], 
      RowBox[{"-", "1.1362269897705704`"}], 
      RowBox[{"-", "0.49029365031147454`"}]},
     {"0.49029365031147454`", "1.1362269897705704`", 
      RowBox[{"-", "0.03440520791863211`"}], "0.13426892237588484`"},
     {
      RowBox[{"-", "1.1362269897705704`"}], "0.49029365031147454`", 
      RowBox[{"-", "0.13426892237588484`"}], 
      RowBox[{"-", "0.03440520791863211`"}]},
     {
      RowBox[{"-", "0.025482421781156797`"}], "0.12248900695820802`", 
      "0.834460740287474`", "0.9157695452133073`"},
     {
      RowBox[{"-", "0.9157695452133073`"}], 
      RowBox[{"-", "0.834460740287474`"}], "0.12248900695820802`", 
      RowBox[{"-", "0.025482421781156797`"}]},
     {"0.834460740287474`", 
      RowBox[{"-", "0.9157695452133073`"}], "0.025482421781156797`", 
      "0.12248900695820802`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588957364*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0.35008901534991677`", "0.0271851147719099`", "0.24591735068245296`", 
      RowBox[{"-", "0.34035331366226135`"}]},
     {"0.02718511477190991`", "0.3513114886073904`", "0.2457888009410154`", 
      RowBox[{"-", "0.3498187063714803`"}]},
     {"0.24591735068245302`", "0.24578880094101535`", "2.5178820565653934`", 
      RowBox[{"-", "3.0561880128300496`"}]},
     {
      RowBox[{"-", "0.3403533136622614`"}], 
      RowBox[{"-", "0.3498187063714803`"}], 
      RowBox[{"-", "3.0561880128300496`"}], "4.620681794504531`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.5478805889606333`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "0.3349613793740621`"}], ",", 
   RowBox[{"-", "0.19538915728470033`"}], ",", "0.5371363322760498`", ",", 
   RowBox[{"-", "0.6733193848689887`"}]}], "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.5478805889635763`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.9030748742593473`", ",", "0.44053598244043757`", ",", 
   RowBox[{"-", "0.6042707934639923`"}], ",", "0.6905219888283047`"}], 
  "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588965823*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1.2085415869279845`", 
      RowBox[{"-", "1.3810439776566095`"}], 
      RowBox[{"-", "1.8061497485186946`"}], 
      RowBox[{"-", "0.8810719648808751`"}]},
     {"0.8810719648808751`", "1.8061497485186946`", 
      RowBox[{"-", "1.3810439776566095`"}], "1.2085415869279845`"},
     {
      RowBox[{"-", "1.8061497485186946`"}], "0.8810719648808751`", 
      RowBox[{"-", "1.2085415869279845`"}], 
      RowBox[{"-", "1.3810439776566095`"}]},
     {
      RowBox[{"-", "0.38862544366810947`"}], "1.81882205645977`", 
      "1.355672096780049`", "1.4523531644921608`"},
     {
      RowBox[{"-", "1.4523531644921608`"}], 
      RowBox[{"-", "1.355672096780049`"}], "1.81882205645977`", 
      RowBox[{"-", "0.38862544366810947`"}]},
     {"1.355672096780049`", 
      RowBox[{"-", "1.4523531644921608`"}], "0.38862544366810947`", 
      "1.81882205645977`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588968705*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0.5641219378813503`", "0.2467896758770379`", "0.36240618996468293`", 
      RowBox[{"-", "0.48978324469524875`"}]},
     {"0.2467896758770379`", "0.1927273858172467`", "0.1794712593227442`", 
      RowBox[{"-", "0.2455868478258115`"}]},
     {"0.36240618996468293`", "0.1794712593227442`", "0.3321301926787157`", 
      RowBox[{"-", "0.35689111758491276`"}]},
     {
      RowBox[{"-", "0.4897832446952487`"}], 
      RowBox[{"-", "0.24558684782581153`"}], 
      RowBox[{"-", "0.35689111758491276`"}], "0.5524211982689773`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588971643*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.19827335865748372`", ",", "0.11338088560498431`", ",", 
   RowBox[{"-", "0.12721278077556664`"}], ",", "0.175361305331258`"}], 
  "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588974208*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.7048015156018635`", ",", "0.32715509683545324`", ",", 
   RowBox[{"-", "0.4770580126884256`"}], ",", "0.5151606834970468`"}], 
  "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.5478805889765873`*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0.9541160253768513`", 
      RowBox[{"-", "1.0303213669940936`"}], 
      RowBox[{"-", "1.409603031203727`"}], 
      RowBox[{"-", "0.6543101936709065`"}]},
     {"0.6543101936709065`", "1.409603031203727`", 
      RowBox[{"-", "1.0303213669940936`"}], "0.9541160253768513`"},
     {
      RowBox[{"-", "1.409603031203727`"}], "0.6543101936709065`", 
      RowBox[{"-", "0.9541160253768513`"}], 
      RowBox[{"-", "1.0303213669940936`"}]},
     {
      RowBox[{"-", "0.3330112412820105`"}], "1.3786070529642729`", 
      "1.0727169132327188`", "1.1067188328782231`"},
     {
      RowBox[{"-", "1.1067188328782231`"}], 
      RowBox[{"-", "1.0727169132327188`"}], "1.3786070529642729`", 
      RowBox[{"-", "0.3330112412820105`"}]},
     {"1.0727169132327188`", 
      RowBox[{"-", "1.1067188328782231`"}], "0.3330112412820105`", 
      "1.3786070529642729`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588979044*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0.9162374264348714`", "0.4267460511363993`", "0.5869588615252631`", 
      RowBox[{"-", "0.8250549396571848`"}]},
     {"0.4267460511363993`", "0.34540694305768516`", "0.3111321999856258`", 
      RowBox[{"-", "0.4426928138324467`"}]},
     {"0.5869588615252631`", "0.3111321999856258`", "0.5436747962537244`", 
      RowBox[{"-", "0.6026960687801071`"}]},
     {
      RowBox[{"-", "0.8250549396571849`"}], 
      RowBox[{"-", "0.4426928138324467`"}], 
      RowBox[{"-", "0.6026960687801071`"}], "0.9657620299046145`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588981893*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.02783035843223801`", ",", "0.019087643952858512`", ",", 
   RowBox[{"-", "0.016191647420501453`"}], ",", "0.029019925328627738`"}], 
  "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.54788058898472*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.6769711571696255`", ",", "0.30806745288259474`", ",", 
   RowBox[{"-", "0.4608663652679242`"}], ",", "0.48614075816841906`"}], 
  "}"}]], "Print",
 CellChangeTimes->{{3.547878857759659*^9, 3.547878885944466*^9}, {
   3.547879285884513*^9, 3.5478793040704117`*^9}, 3.547879354249016*^9, {
   3.5478805690671053`*^9, 3.547880588986932*^9}}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"parmin", "[", 
  RowBox[{"[", "2", "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.5478788985946074`*^9, 3.547878905482736*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"q0", "\[Rule]", 
    RowBox[{"-", "0.6763419955558382`"}]}], ",", 
   RowBox[{"q1", "\[Rule]", 
    RowBox[{"-", "0.30749670819054215`"}]}], ",", 
   RowBox[{"q2", "\[Rule]", "0.4607080988205089`"}], ",", 
   RowBox[{"q3", "\[Rule]", 
    RowBox[{"-", "0.4854252669876748`"}]}]}], "}"}]], "Output",
 CellChangeTimes->{3.547878905875711*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Release", "[", 
  RowBox[{"QuatToEuler", "[", 
   RowBox[{"{", 
    RowBox[{"0.6769711571696255`", ",", "0.30806745288259474`", ",", 
     RowBox[{"-", "0.4608663652679242`"}], ",", "0.48614075816841906`"}], 
    "}"}], "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.547878954899983*^9, 3.5478789768255167`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1.1517412130806859`", ",", 
   RowBox[{"-", "0.33043886597300787`"}], ",", "1.4623896236189386`"}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.547878971213819*^9, 3.547878977373218*^9}}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.5478787896908607`*^9, 3.5478788107881823`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Release", "[", 
  RowBox[{"QuatToEuler", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"q0", ",", "q1", ",", "q2", ",", "q3"}], "}"}], "/.", 
    RowBox[{"parmin", "[", 
     RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1.1499320016362513`", ",", 
   RowBox[{"-", "0.33065131005050385`"}], ",", "1.4603694917826469`"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.547879012460622*^9}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.547878809169526*^9, 3.547878809194305*^9}}],

Cell[CellGroupData[{

Cell[BoxData["parmin"], "Input",
 CellChangeTimes->{{3.5478787991453114`*^9, 3.547878802372381*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0.00047056188082167475`", ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"q0", "\[Rule]", 
      RowBox[{"-", "0.6763419955558382`"}]}], ",", 
     RowBox[{"q1", "\[Rule]", 
      RowBox[{"-", "0.30749670819054215`"}]}], ",", 
     RowBox[{"q2", "\[Rule]", "0.4607080988205089`"}], ",", 
     RowBox[{"q3", "\[Rule]", 
      RowBox[{"-", "0.4854252669876748`"}]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.5478788027302732`*^9}]
}, Open  ]],

Cell[BoxData["2"], "Input",
 CellChangeTimes->{3.547878148846251*^9}],

Cell[CellGroupData[{

Cell[BoxData["J1"], "Input",
 CellChangeTimes->{{3.547877082318161*^9, 3.547877082592936*^9}, {
  3.5478771375816936`*^9, 3.547877137763332*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1.`", ",", 
   RowBox[{"-", "1.`"}], ",", "1.`", ",", "0.4892248516665787`", ",", 
   RowBox[{"-", "0.4892248516665787`"}], ",", "0.345234342277412`"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.547877082917301*^9, 3.547877138091353*^9}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.54787710484212*^9, 3.5478771825042887`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Transpose", "[", "J", "]"}], ".", "J"}]], "Input",
 CellChangeTimes->{{3.547877186088944*^9, 3.547877189734371*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"3.597868662064089`", ",", 
     RowBox[{"-", "1.1688972198908758`"}], ",", "1.1688972198908758`", ",", 
     RowBox[{"-", "1.1191867510877174`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1.1688972198908758`"}], ",", "3.4777144576636205`", ",", 
     "1.239340955488186`", ",", 
     RowBox[{"-", "1.1688972198908758`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
    "1.1688972198908758`", ",", "1.239340955488186`", ",", 
     "3.4777144576636205`", ",", "1.1688972198908758`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1.1191867510877174`"}], ",", 
     RowBox[{"-", "1.1688972198908758`"}], ",", "1.1688972198908758`", ",", 
     "3.597868662064089`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.547877190201562*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["yref"], "Input",
 CellChangeTimes->{{3.547876936994048*^9, 3.547876938144617*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0", ",", "0", ",", "1", ",", "0.`", ",", 
   RowBox[{"-", "0.07199525469458334`"}], ",", "0.41722959697199535`"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.5478769383778553`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.547885118063937*^9, 3.547885148683824*^9}}],

Cell[BoxData["0.9812000000000001`"], "Output",
 CellChangeTimes->{3.5478851270962267`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ArcTan", "[", 
  RowBox[{
   RowBox[{"Sqrt", "[", 
    RowBox[{
     RowBox[{"0.32", "^", "2"}], "+", 
     RowBox[{"0.18", "^", "2"}]}], "]"}], "/", "0.92"}], "]"}]], "Input",
 CellChangeTimes->{{3.54788514315051*^9, 3.547885175379054*^9}}],

Cell[BoxData["0.37971076716646646`"], "Output",
 CellChangeTimes->{{3.547885157750087*^9, 3.547885175976117*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"%", "/", "Pi"}], "*", "180"}]], "Input",
 CellChangeTimes->{{3.5478851782860928`*^9, 3.5478851804824123`*^9}}],

Cell[BoxData["21.7558243943132`"], "Output",
 CellChangeTimes->{3.5478851808755503`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"90", "-", "%"}]], "Input",
 CellChangeTimes->{{3.5478851827052937`*^9, 3.5478851834909687`*^9}}],

Cell[BoxData["68.24417560568679`"], "Output",
 CellChangeTimes->{3.547885183805627*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Pi", "//", "N"}]], "Input",
 CellChangeTimes->{{3.547885282544238*^9, 3.5478852832722197`*^9}}],

Cell[BoxData["3.141592653589793`"], "Output",
 CellChangeTimes->{3.547885283546708*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"0.9304", "^", "2"}], "+", 
  RowBox[{"0.3657", "^", "2"}], "+", 
  RowBox[{"0.0223", "^", "2"}], "+", 
  RowBox[{"0.0087", "^", "2"}]}]], "Input",
 CellChangeTimes->{{3.547927812512686*^9, 3.5479278306003304`*^9}}],

Cell[BoxData["0.9999536299999999`"], "Output",
 CellChangeTimes->{3.5479278319193993`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"0.9167", "^", "2"}], "+", 
  RowBox[{"0.3548", "^", "2"}], "+", 
  RowBox[{"0.0245", "^", "2"}], "+", 
  RowBox[{"0.0018", "^", "2"}]}]], "Input",
 CellChangeTimes->{{3.547927833651658*^9, 3.547927849863553*^9}}],

Cell[BoxData["0.9668254199999999`"], "Output",
 CellChangeTimes->{3.547927850218749*^9}]
}, Open  ]]
},
WindowSize->{819, 767},
WindowMargins->{{Automatic, 7}, {29, Automatic}},
FrontEndVersion->"8.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (November 6, \
2010)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 205, 4, 43, "Input"],
Cell[765, 26, 176, 3, 43, "Input"],
Cell[944, 31, 957, 28, 148, "Input"],
Cell[1904, 61, 605, 17, 43, "Input"],
Cell[2512, 80, 117, 2, 27, "Input"],
Cell[CellGroupData[{
Cell[2654, 86, 265, 5, 27, "Input"],
Cell[2922, 93, 349, 8, 33, "Output"]
}, Open  ]],
Cell[3286, 104, 164, 2, 27, "Input"],
Cell[CellGroupData[{
Cell[3475, 110, 220, 4, 27, "Input"],
Cell[3698, 116, 356, 8, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4091, 129, 161, 3, 27, "Input"],
Cell[4255, 134, 502, 14, 33, "Output"]
}, Open  ]],
Cell[4772, 151, 525, 15, 58, "Input"],
Cell[5300, 168, 1342, 38, 118, "Input"],
Cell[CellGroupData[{
Cell[6667, 210, 1968, 52, 193, "Input"],
Cell[8638, 264, 121, 2, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8796, 271, 99, 1, 27, "Input"],
Cell[8898, 274, 1473, 23, 103, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10408, 302, 125, 2, 27, "Input"],
Cell[10536, 306, 88, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10661, 312, 140, 2, 27, "Input"],
Cell[10804, 316, 115, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10956, 322, 123, 2, 27, "Input"],
Cell[11082, 326, 80, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[11199, 332, 96, 1, 27, "Input"],
Cell[11298, 335, 283, 6, 33, "Output"]
}, Open  ]],
Cell[11596, 344, 1121, 32, 43, "Input"],
Cell[CellGroupData[{
Cell[12742, 380, 310, 7, 27, "Input"],
Cell[13055, 389, 1153, 23, 231, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[14245, 417, 127, 2, 27, "Input"],
Cell[14375, 421, 230, 5, 27, "Output"]
}, Open  ]],
Cell[14620, 429, 643, 20, 43, "Input"],
Cell[CellGroupData[{
Cell[15288, 453, 332, 10, 27, "Input"],
Cell[15623, 465, 111, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15771, 471, 120, 2, 27, "Input"],
Cell[15894, 475, 88, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16019, 481, 121, 2, 27, "Input"],
Cell[16143, 485, 123, 2, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16303, 492, 100, 1, 27, "Input"],
Cell[16406, 495, 78, 1, 27, "Output"]
}, Open  ]],
Cell[16499, 499, 8183, 239, 673, "Input"],
Cell[CellGroupData[{
Cell[24707, 742, 175, 4, 27, "Input"],
Cell[24885, 748, 279, 5, 33, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25201, 758, 170, 3, 27, "Input"],
Cell[25374, 763, 284, 6, 33, "Output"]
}, Open  ]],
Cell[25673, 772, 232, 4, 43, "Input"],
Cell[CellGroupData[{
Cell[25930, 780, 443, 12, 27, "Input"],
Cell[26376, 794, 303, 6, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[26716, 805, 95, 1, 27, "Input"],
Cell[26814, 808, 286, 5, 27, "Output"]
}, Open  ]],
Cell[27115, 816, 145, 3, 27, "Input"],
Cell[27263, 821, 880, 27, 27, "Input"],
Cell[28146, 850, 582, 14, 43, "Input"],
Cell[CellGroupData[{
Cell[28753, 868, 96, 1, 27, "Input"],
Cell[28852, 871, 22290, 623, 776, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[51179, 1499, 131, 2, 27, "Input"],
Cell[51313, 1503, 21597, 541, 405, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[72947, 2049, 125, 2, 27, "Input"],
Cell[73075, 2053, 225, 6, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[73337, 2064, 123, 2, 27, "Input"],
Cell[73463, 2068, 276, 7, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[73776, 2080, 224, 5, 27, "Input"],
Cell[74003, 2087, 112, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[74152, 2093, 116, 2, 27, "Input"],
Cell[74271, 2097, 95, 1, 27, "Output"]
}, Open  ]],
Cell[74381, 2101, 331, 9, 27, "Input"],
Cell[74715, 2112, 220, 6, 27, "Input"],
Cell[CellGroupData[{
Cell[74960, 2122, 121, 2, 27, "Input"],
Cell[75084, 2126, 7084, 212, 189, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[82205, 2343, 410, 11, 27, "Input"],
Cell[82618, 2356, 60258, 1023, 367, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[142913, 3384, 177, 4, 27, "Input"],
Cell[143093, 3390, 450, 8, 33, "Output"]
}, Open  ]],
Cell[143558, 3401, 2606, 77, 73, "Input"],
Cell[146167, 3480, 95, 1, 27, "Input"],
Cell[CellGroupData[{
Cell[146287, 3485, 374, 9, 27, "Input"],
Cell[146664, 3496, 318, 7, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[147019, 3508, 200, 5, 27, InheritFromParent],
Cell[147222, 3515, 200, 5, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[147459, 3525, 168, 3, 27, "Input"],
Cell[147630, 3530, 425, 9, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[148092, 3544, 69, 1, 27, "Input"],
Cell[148164, 3547, 7109, 213, 189, "Output"]
}, Open  ]],
Cell[155288, 3763, 201, 5, 27, "Input"],
Cell[CellGroupData[{
Cell[155514, 3772, 94, 1, 27, "Input"],
Cell[155611, 3775, 25139, 538, 1333, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[180787, 4318, 341, 9, 43, "Input"],
Cell[181131, 4329, 327, 6, 33, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[181495, 4340, 298, 6, 27, InheritFromParent],
Cell[181796, 4348, 266, 5, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[182099, 4358, 144, 3, 27, "Input"],
Cell[182246, 4363, 95, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[182378, 4369, 202, 5, 27, "Input"],
Cell[182583, 4376, 351, 6, 33, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[182971, 4387, 95, 1, 27, "Input"],
Cell[183069, 4390, 260, 5, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[183366, 4400, 96, 1, 27, "Input"],
Cell[183465, 4403, 247, 6, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[183749, 4414, 249, 5, 27, "Input"],
Cell[184001, 4421, 248, 6, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[184286, 4432, 694, 20, 27, "Input"],
Cell[184983, 4454, 273, 7, 27, "Output"]
}, Open  ]],
Cell[185271, 4464, 2770, 81, 103, "Input"],
Cell[188044, 4547, 94, 1, 27, "Input"],
Cell[CellGroupData[{
Cell[188163, 4552, 430, 11, 43, "Input"],
Cell[188596, 4565, 1720, 56, 73, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[190353, 4626, 129, 2, 27, "Input"],
Cell[190485, 4630, 2100, 66, 81, "Output"]
}, Open  ]],
Cell[192600, 4699, 575, 15, 27, "Input"],
Cell[CellGroupData[{
Cell[193200, 4718, 146, 3, 27, "Input"],
Cell[193349, 4723, 72, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[193458, 4729, 96, 1, 27, "Input"],
Cell[193557, 4732, 244, 5, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[193838, 4742, 275, 7, 27, "Input"],
Cell[194116, 4751, 264, 6, 27, "Output"]
}, Open  ]],
Cell[194395, 4760, 129, 3, 27, "Input"],
Cell[CellGroupData[{
Cell[194549, 4767, 666, 18, 58, "Input"],
Cell[195218, 4787, 3177, 84, 92, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[198432, 4876, 757, 22, 43, "Input"],
Cell[199192, 4900, 5606, 163, 223, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[204835, 5068, 120, 2, 27, "Input"],
Cell[204958, 5072, 476, 10, 23, "Message"],
Cell[205437, 5084, 6134, 185, 223, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[211608, 5274, 98, 1, 27, "Input"],
Cell[211709, 5277, 248, 5, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[211994, 5287, 8737, 233, 388, "Input"],
Cell[CellGroupData[{
Cell[220756, 5524, 1419, 38, 102, "Print"],
Cell[222178, 5564, 1315, 30, 70, "Print"],
Cell[223496, 5596, 380, 7, 20, "Print"],
Cell[223879, 5605, 384, 7, 20, "Print"],
Cell[224266, 5614, 1629, 38, 102, "Print"],
Cell[225898, 5654, 1277, 28, 70, "Print"],
Cell[227178, 5684, 416, 8, 20, "Print"],
Cell[227597, 5694, 379, 7, 20, "Print"],
Cell[227979, 5703, 1608, 38, 102, "Print"],
Cell[229590, 5743, 1276, 28, 70, "Print"],
Cell[230869, 5773, 380, 7, 20, "Print"],
Cell[231252, 5782, 381, 7, 20, "Print"],
Cell[231636, 5791, 1611, 38, 102, "Print"],
Cell[233250, 5831, 1271, 28, 70, "Print"],
Cell[234524, 5861, 384, 7, 20, "Print"],
Cell[234911, 5870, 380, 7, 20, "Print"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[235340, 5883, 150, 3, 27, "Input"],
Cell[235493, 5888, 392, 10, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[235922, 5903, 335, 7, 43, "Input"],
Cell[236260, 5912, 226, 5, 27, "Output"]
}, Open  ]],
Cell[236501, 5920, 96, 1, 27, "Input"],
Cell[CellGroupData[{
Cell[236622, 5925, 259, 7, 27, "Input"],
Cell[236884, 5934, 202, 5, 27, "Output"]
}, Open  ]],
Cell[237101, 5942, 92, 1, 27, InheritFromParent],
Cell[CellGroupData[{
Cell[237218, 5947, 100, 1, 27, "Input"],
Cell[237321, 5950, 479, 12, 27, "Output"]
}, Open  ]],
Cell[237815, 5965, 69, 1, 27, "Input"],
Cell[CellGroupData[{
Cell[237909, 5970, 145, 2, 27, "Input"],
Cell[238057, 5974, 277, 6, 27, "Output"]
}, Open  ]],
Cell[238349, 5983, 93, 1, 27, "Input"],
Cell[CellGroupData[{
Cell[238467, 5988, 151, 3, 27, "Input"],
Cell[238621, 5993, 844, 21, 43, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[239502, 6019, 96, 1, 27, "Input"],
Cell[239601, 6022, 219, 5, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[239857, 6032, 92, 1, 27, "Input"],
Cell[239952, 6035, 90, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[240079, 6041, 265, 7, 27, "Input"],
Cell[240347, 6050, 113, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[240497, 6056, 145, 3, 27, "Input"],
Cell[240645, 6061, 88, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[240770, 6067, 120, 2, 27, "Input"],
Cell[240893, 6071, 87, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[241017, 6077, 119, 2, 27, "Input"],
Cell[241139, 6081, 87, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[241263, 6087, 249, 6, 27, "Input"],
Cell[241515, 6095, 90, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[241642, 6101, 247, 6, 27, "Input"],
Cell[241892, 6109, 88, 1, 27, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
